A coin is tossed and a dice is thrown. Write down the probability of obtaining: 

1. a ‘head’ on the coin.
2. an odd number on the dice.
3. a 'head' on the coin and an odd number on the dice.

Box A contains 3 red balls and 3 white balls. Box B contains 1 red and 4 white balls. One ball is randomly selected from Box A and one from Box B. What is the probability that both balls selected are red?

In an experiment, a card is drawn from a pack of playing cards, and a dice is thrown. Find the probability of obtaining:

1. a card which is an ace and a six on the dice,
2. the king of clubs and an even number on the dice,
3. a heart and a 'one' on the dice.

A ball is selected at random from a bag containing 3 red balls, 4 black balls, and 5 green balls. The first ball is replaced and a second is selected. Find the probability of obtaining:

1. two red balls,
2. two green balls.

The letters of the word 'INDEPENDENT are written on individual cards and the cards are put into a box. A card is selected and then replaced and then a second card is selected. Find the probability of obtaining:

1. the letter 'P' twice,
2. the letter 'E' twice.

Philip and his sister toss a coin to decide who does the washing up. If it's heads Philip does it. If it's tails his sister does it, what is the probability that Philip does the washing up every day for a week (7 days)?

A card is drawn at random from a pack of 52 playing cards, the card is replaced and a second card is drawn. This card is replaced and a third is drawn. What is the probability of drawing:

1. three hearts?
2. at least two hearts?
3. exactly one heart?

There is a spinner that has six equal sectors: the equal sectors comprise words P, Q, R, S, T and U. Find the probability of getting:

1. 20 Qs in 20 trials
2. No Qs in n trials
3. At least one Q in n trials.

A cubical dice and a coin are thrown together at once, find the probability of getting ‘5’ on dice and ‘head’ on coin.

What is the probability of getting 3 on the dice and head on the coin when a dice is rolled and a coin is tossed simultaneously?

Pot A contains 3 red balls and 1 white ball. Pot B contains 2 red balls and 3 white balls. A ball is chosen at random from each bag in turn. Find the probability of taking:

1. a white ball from each pot.
2. two balls of the same colour.

There are 1000 components in a box of which 10 are known to be defective. Two components are selected at random. What is the probability that:

1. both are defective
2. neither are defective
3. just one is defective? (Do not simplify your answer)

A pot contains 3 red, 4 white, and 5 green balls. Two balls are selected without replacement. Find the probability that the three balls chosen are:

1. all red.
2. all green.
3. one of each colour.
4. If the selection of the two balls was carried out 1100 times, how often would you expect to choose two red balls?

There are 9 boys and 15 girls in a class. Three children are chosen at random. What is the probability that

1. all three are boys?
2. all three are girls?
3. one is a boy and two are girls. Give your answers as fractions.

A box contains x milk chocolates and y plain chocolates. Two chocolates are selected at random Find, in terms of x and y, the probability of choosing:

1. a milk chocolate on the first choice
2. two milk chocolates 
3. one of each sort
4. two plain chocolates

A bag contains 10 discs; 7 are black and 3 are white. A disc is selected and then replaced. A second disc is selected. Complete the tree diagram showing all the probabilities and outcomes. Find the probability of the following:

1. both discs are black.
2. both discs are white.

A bag contains 5 red balls and 3 green balls. A ball is drawn and then replaced before another ball is drawn. Find the probability by using a tree diagram that:

1. two green balls are drawn.
2. the first ball is red and the second is green.

A bag contains 7 green discs and 3 blue discs. A disc is drawn and not replaced. A second disc is drawn. Draw a tree diagram. Find the probability that:

1. both discs are green
2. both discs are blue

A pot contains 4 red balls, 2 green balls, and 3 blue balls. A ball is drawn and not replaced. A second ball is drawn. Find the probability of drawing:

1. two blue balls
2. two red balls
3. one red ball and one blue ball (in any order).
4. one green ball and one red ball (in any order).

A six-sided dice is thrown three times. Draw a tree diagram, showing at each branch the two events: 'three' and 'not three' (written 3'). What is the probability of throwing a total of

1. three threes,
2. no threes,
3. one three,
4. at least one three?

A bag contains 6 red marbles and 4 yellow marbles. A marble is drawn at random and replaced. Two further draws are made, again without replacement. Find the probability of drawing:

1. three red marbles,
2. three yellow marbles,
3. no red marbles,
4. at least one red marble.

From a bag containing 4 red and 7 blue balls of the same shape and size, two balls are drawn randomly in succession without replacement. Show the probabilities of all outcomes in a tree diagram.

From a bag containing 5 yellow and 6 blue balls of the same shape and size, two balls are drawn randomly in succession without replacement. Show the probabilities of all outcomes on a tree diagram.

From a class having 24 boys and 15 girls, two students are selected randomly. Show all the probabilities of being a boy and a girl on a tree diagram.

A class contains 20 boys and 30 girls. If two students are selected at random, show the probability of selecting a boy and a girl on a tree diagram.

From a bag containing one red, one green, and one yellow ball of the same shape and size, two balls are drawn randomly in succession without replacement. Show the probabilities of all outcomes in a tree diagram.

Two cards are drawn one after the another (without replacement) from a well shuffled pack of 52 playing cards. Show the probability of getting or not getting a king by drawing a tree diagram.

There is one yellow, one red and one black sweet in a bag. A sweet is taken out randomly and not replaced. Then after, another sweet is drawn. Write a sample space by using a tree diagram.

Two cards are drawn from a well-shuffled deck of 52 cards. Find the probability that both cards are king (the first card is not replaced) by drawing a tree diagram.

Two children were born from a married couple.

1. Find the probability of having at least one son by drawing a tree diagram.
2. By drawing a tree diagram, find the probability of having no daughter

A bag contains 3 red and 2 blue balls of the same shape and size.

1. State the addition law of probability.
2. Two balls are drawn randomly one after another with replacement. Show the probabilities of all events of getting red or blue balls in a tree diagram.
3. Find the probability of getting the first ball red and the second ball blue without replacement.
4. What is the difference between the probability of both balls being blue if two balls are drawn one after the other with replacement or without replacement?

A bag contains 9 red and 6 blue balls of the same shape and size.

1. State the multiplication law of probability.
2. Two balls are drawn randomly one after another with replacement. Show the probabilities of all events of getting red or blue balls in a tree diagram.
3. Find the probability of getting the first ball red and the second ball blue without replacement.
4. What is the difference between the probability of both balls being blue if two balls are drawn one after the other with replacement or without replacement?

An unbiased die is thrown. Find the probability of getting the following event.

1. Define mutually exclusive events.
2. A number 3 or 4.
3. A number between 3 and 6.
4. Odd number or even number.
5. If the dice is thrown twice, then find the probability of getting both the prime numbers.

Two unbiased coins are tossed simultaneously.

1. Define independent event in probability.
2. Draw a probability tree diagram of the experiment.
3. Write the sample space.
4. Find the probability of getting two heads.
5. Find the probability of getting at least one head.
6. Find the probability of getting at most one head.
7. Find the probability of getting the same events.

Three coins are tossed together.

1. Define the addition law of probability for mutually exclusive events.
2. Draw a tree diagram to represent the possible outcomes.
3. Write the sample space.

Find the probability of getting the following events:

1. All heads
2. Two heads 
3. One head
4. At least three heads
5. Same kind

A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting the following cards. 

1. Queen or king
2. Face card or ace
3. Black or diamond
4. Red or club

From number cards written from 1 to 25 one card is chosen at random. Find the following probabilities of getting

1. Multiples of 4 or multiples of 7.
2. Odd or multiples of 4.
3. Even or multiples of 5.
4. Composite numbers or prime numbers greater than 10.

In a bag, there are 3 balls each of colour red, white and black. If a ball is drawn.

1. Find the probability of getting a white ball and a black ball
2. Find the probability of getting either red or white ball.
3. Find the probability of getting either black or red ball.
4. Find the probability of getting neither red nor black ball.

There is a coin and a dice. A coin is tossed and a die is rolled simultaneously. Find the probability of getting the following events.

1. Tail and 4.
2. Head and 5.
3. Tail and even numbers
4. Head and odd numbers.
5. Head or prime numbers.
6. Tail or even numbers

X and Y are two mutually exclusive events. If $\rm P(X) = \frac {1}{8}$ and $\rm P(Y) = \frac {5}{24}$.

1. Find $\rm P(X \cup Y)$.
2. Find $\rm P \overline{ (X \cup Y)}$. 

A bag contains 5 red balls and 3 blue balls. A ball is drawn at random and not replaced. Then another ball is drawn.

1. Draw a tree diagram to show all the possible outcomes.
2. Find the probability that both balls are blue.
3. Find the probability that both balls are red.
4. Find the probability of getting both are of same colour.
5. Find the probability of getting both are of different colour.
6. Find the probability of getting at least one red.
7. Find the probability of getting at most one blue.

There is one red, one white, and one yellow sweet in a pot. A sweet is taken out randomly and not replaced. Then another sweet is drawn.

1. Draw a tree diagram to show all the possible outcomes.
2. Write the sample space of the experiment.
3. Find the probability of getting red and white sweet.
4. Find the probability of getting at least one red sweet.

A coin is tossed two times.

1. Draw a tree diagram to represent all the possible outcomes.
2. Write the sample space.
3. Find the probability that both are heads.
4. Find the probability that both are tails.
5. Find the probability of getting the same kind of events.
6. Find the probability of getting at least one head.

Three children are born in a family.

1. Draw a tree diagram to represent all the possible outcomes.
2. Write down the sample space of the experiment.
3. Find the probability of being all three sons
4. Find the probability of being all three daughters
5. Find the probability of being at least one son.
6. Find the probability of being two sons and one daughter.
7. Find the probability of being one son and two daughters.

A queen of heart is absent in a well-shuffled pack of playing cards.

1. Draw a tree diagram to show all the possible outcomes.
2. What is the probability of getting both the kings if two cards are drawn at random?
3. Find the probability of getting both are other than king.
4. Find the probability of getting king in the first time and non-king in the second time.

From a class having 12 boys and 18 girls, two students are selected randomly without sending the first student back to the class.

1. Define mutually exclusive events.
2. Show the probabilities of possible outcomes of selecting boys and girls in a tree diagram.
3. Find the probability of selecting both girls.
4. By how much the probability of getting at least one boy is less than the total probability? Calculate it.

The monthly consumption of electricity (in units) of 50 consumers is given in the table below.

1. Write the formula to find the median of a continuous series.
2. Find the modal class and median class of the given data.
3. Calculate the median of the given data.
4. Did you find the modal class and median class same from the above computation? Are they always same? Give reason.

The weight of 20 students is presented here in the table.

1. In a continuous series, what does m represent in the formula ($\rm\overline X$)=$\rm \frac {\sum fm}{N}$ to calculate mean? Write it. 
2. Find the median class of the given data.
3. Calculate the average weight from the given data.
4. Is the class of measure of central tendencies of the given data same? Justify it. 

There are 1 red, 1 black and 1 white ball of the same shape and size in a bag. Two balls are drawn randomly one after another without replacement.

1. If A and B are two independent events, write the formula of P(A $\rm \cap$ B).
2. Show the probability of all the possible outcomes in a probability tree diagram. 
3. Find the probability of getting a red ball and a black ball. 
4. Is there any possibility of getting both balls of the same color? Give reason.

Which of the following statistical methods is not a measure of central tendency?

If a coin is tossed n times, what is its sample space?

A coin is tossed and a dice is thrown. Write down the probability of obtaining: 

1. a ‘head’ on the coin.
2. an odd number on the dice.
3. a 'head' on the coin and an odd number on the dice.

Box A contains 3 red balls and 3 white balls. Box B contains 1 red and 4 white balls. One ball is randomly selected from Box A and one from Box B. What is the probability that both balls selected are red?

In an experiment, a card is drawn from a pack of playing cards, and a dice is thrown. Find the probability of obtaining:

1. a card which is an ace and a six on the dice,
2. the king of clubs and an even number on the dice,
3. a heart and a 'one' on the dice.

A ball is selected at random from a bag containing 3 red balls, 4 black balls, and 5 green balls. The first ball is replaced and a second is selected. Find the probability of obtaining:

1. two red balls,
2. two green balls.

The letters of the word 'INDEPENDENT are written on individual cards and the cards are put into a box. A card is selected and then replaced and then a second card is selected. Find the probability of obtaining:

1. the letter 'P' twice,
2. the letter 'E' twice.

Philip and his sister toss a coin to decide who does the washing up. If it's heads Philip does it. If it's tails his sister does it, what is the probability that Philip does the washing up every day for a week (7 days)?

A card is drawn at random from a pack of 52 playing cards, the card is replaced and a second card is drawn. This card is replaced and a third is drawn. What is the probability of drawing:

1. three hearts?
2. at least two hearts?
3. exactly one heart?

There is a spinner that has six equal sectors: the equal sectors comprise words P, Q, R, S, T and U. Find the probability of getting:

1. 20 Qs in 20 trials
2. No Qs in n trials
3. At least one Q in n trials.

A cubical dice and a coin are thrown together at once, find the probability of getting ‘5’ on dice and ‘head’ on coin.

What is the probability of getting 3 on the dice and head on the coin when a dice is rolled and a coin is tossed simultaneously?

Pot A contains 3 red balls and 1 white ball. Pot B contains 2 red balls and 3 white balls. A ball is chosen at random from each bag in turn. Find the probability of taking:

1. a white ball from each pot.
2. two balls of the same colour.

There are 1000 components in a box of which 10 are known to be defective. Two components are selected at random. What is the probability that:

1. both are defective
2. neither are defective
3. just one is defective? (Do not simplify your answer)

A pot contains 3 red, 4 white, and 5 green balls. Two balls are selected without replacement. Find the probability that the three balls chosen are:

1. all red.
2. all green.
3. one of each colour.
4. If the selection of the two balls was carried out 1100 times, how often would you expect to choose two red balls?

There are 9 boys and 15 girls in a class. Three children are chosen at random. What is the probability that

1. all three are boys?
2. all three are girls?
3. one is a boy and two are girls. Give your answers as fractions.

A box contains x milk chocolates and y plain chocolates. Two chocolates are selected at random Find, in terms of x and y, the probability of choosing:

1. a milk chocolate on the first choice
2. two milk chocolates 
3. one of each sort
4. two plain chocolates

A bag contains 10 discs; 7 are black and 3 are white. A disc is selected and then replaced. A second disc is selected. Complete the tree diagram showing all the probabilities and outcomes. Find the probability of the following:

1. both discs are black.
2. both discs are white.

A bag contains 5 red balls and 3 green balls. A ball is drawn and then replaced before another ball is drawn. Find the probability by using a tree diagram that:

1. two green balls are drawn.
2. the first ball is red and the second is green.

A bag contains 7 green discs and 3 blue discs. A disc is drawn and not replaced. A second disc is drawn. Draw a tree diagram. Find the probability that:

1. both discs are green
2. both discs are blue

A pot contains 4 red balls, 2 green balls, and 3 blue balls. A ball is drawn and not replaced. A second ball is drawn. Find the probability of drawing:

1. two blue balls
2. two red balls
3. one red ball and one blue ball (in any order).
4. one green ball and one red ball (in any order).

A six-sided dice is thrown three times. Draw a tree diagram, showing at each branch the two events: 'three' and 'not three' (written 3'). What is the probability of throwing a total of

1. three threes,
2. no threes,
3. one three,
4. at least one three?

A bag contains 6 red marbles and 4 yellow marbles. A marble is drawn at random and replaced. Two further draws are made, again without replacement. Find the probability of drawing:

1. three red marbles,
2. three yellow marbles,
3. no red marbles,
4. at least one red marble.

From a bag containing 4 red and 7 blue balls of the same shape and size, two balls are drawn randomly in succession without replacement. Show the probabilities of all outcomes in a tree diagram.

From a bag containing 5 yellow and 6 blue balls of the same shape and size, two balls are drawn randomly in succession without replacement. Show the probabilities of all outcomes on a tree diagram.

From a class having 24 boys and 15 girls, two students are selected randomly. Show all the probabilities of being a boy and a girl on a tree diagram.

A class contains 20 boys and 30 girls. If two students are selected at random, show the probability of selecting a boy and a girl on a tree diagram.

From a bag containing one red, one green, and one yellow ball of the same shape and size, two balls are drawn randomly in succession without replacement. Show the probabilities of all outcomes in a tree diagram.

Two cards are drawn one after the another (without replacement) from a well shuffled pack of 52 playing cards. Show the probability of getting or not getting a king by drawing a tree diagram.

There is one yellow, one red and one black sweet in a bag. A sweet is taken out randomly and not replaced. Then after, another sweet is drawn. Write a sample space by using a tree diagram.

Two cards are drawn from a well-shuffled deck of 52 cards. Find the probability that both cards are king (the first card is not replaced) by drawing a tree diagram.

Two children were born from a married couple.

1. Find the probability of having at least one son by drawing a tree diagram.
2. By drawing a tree diagram, find the probability of having no daughter

A bag contains 3 red and 2 blue balls of the same shape and size.

1. State the addition law of probability.
2. Two balls are drawn randomly one after another with replacement. Show the probabilities of all events of getting red or blue balls in a tree diagram.
3. Find the probability of getting the first ball red and the second ball blue without replacement.
4. What is the difference between the probability of both balls being blue if two balls are drawn one after the other with replacement or without replacement?

A bag contains 9 red and 6 blue balls of the same shape and size.

1. State the multiplication law of probability.
2. Two balls are drawn randomly one after another with replacement. Show the probabilities of all events of getting red or blue balls in a tree diagram.
3. Find the probability of getting the first ball red and the second ball blue without replacement.
4. What is the difference between the probability of both balls being blue if two balls are drawn one after the other with replacement or without replacement?

An unbiased die is thrown. Find the probability of getting the following event.

1. Define mutually exclusive events.
2. A number 3 or 4.
3. A number between 3 and 6.
4. Odd number or even number.
5. If the dice is thrown twice, then find the probability of getting both the prime numbers.

Two unbiased coins are tossed simultaneously.

1. Define independent event in probability.
2. Draw a probability tree diagram of the experiment.
3. Write the sample space.
4. Find the probability of getting two heads.
5. Find the probability of getting at least one head.
6. Find the probability of getting at most one head.
7. Find the probability of getting the same events.

Three coins are tossed together.

1. Define the addition law of probability for mutually exclusive events.
2. Draw a tree diagram to represent the possible outcomes.
3. Write the sample space.

Find the probability of getting the following events:

1. All heads
2. Two heads 
3. One head
4. At least three heads
5. Same kind

A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting the following cards. 

1. Queen or king
2. Face card or ace
3. Black or diamond
4. Red or club

From number cards written from 1 to 25 one card is chosen at random. Find the following probabilities of getting

1. Multiples of 4 or multiples of 7.
2. Odd or multiples of 4.
3. Even or multiples of 5.
4. Composite numbers or prime numbers greater than 10.

In a bag, there are 3 balls each of colour red, white and black. If a ball is drawn.

1. Find the probability of getting a white ball and a black ball
2. Find the probability of getting either red or white ball.
3. Find the probability of getting either black or red ball.
4. Find the probability of getting neither red nor black ball.

There is a coin and a dice. A coin is tossed and a die is rolled simultaneously. Find the probability of getting the following events.

1. Tail and 4.
2. Head and 5.
3. Tail and even numbers
4. Head and odd numbers.
5. Head or prime numbers.
6. Tail or even numbers

X and Y are two mutually exclusive events. If $\rm P(X) = \frac {1}{8}$ and $\rm P(Y) = \frac {5}{24}$.

1. Find $\rm P(X \cup Y)$.
2. Find $\rm P \overline{ (X \cup Y)}$. 

A bag contains 5 red balls and 3 blue balls. A ball is drawn at random and not replaced. Then another ball is drawn.

1. Draw a tree diagram to show all the possible outcomes.
2. Find the probability that both balls are blue.
3. Find the probability that both balls are red.
4. Find the probability of getting both are of same colour.
5. Find the probability of getting both are of different colour.
6. Find the probability of getting at least one red.
7. Find the probability of getting at most one blue.

There is one red, one white, and one yellow sweet in a pot. A sweet is taken out randomly and not replaced. Then another sweet is drawn.

1. Draw a tree diagram to show all the possible outcomes.
2. Write the sample space of the experiment.
3. Find the probability of getting red and white sweet.
4. Find the probability of getting at least one red sweet.

A coin is tossed two times.

1. Draw a tree diagram to represent all the possible outcomes.
2. Write the sample space.
3. Find the probability that both are heads.
4. Find the probability that both are tails.
5. Find the probability of getting the same kind of events.
6. Find the probability of getting at least one head.

Three children are born in a family.

1. Draw a tree diagram to represent all the possible outcomes.
2. Write down the sample space of the experiment.
3. Find the probability of being all three sons
4. Find the probability of being all three daughters
5. Find the probability of being at least one son.
6. Find the probability of being two sons and one daughter.
7. Find the probability of being one son and two daughters.

A queen of heart is absent in a well-shuffled pack of playing cards.

1. Draw a tree diagram to show all the possible outcomes.
2. What is the probability of getting both the kings if two cards are drawn at random?
3. Find the probability of getting both are other than king.
4. Find the probability of getting king in the first time and non-king in the second time.

From a class having 12 boys and 18 girls, two students are selected randomly without sending the first student back to the class.

1. Define mutually exclusive events.
2. Show the probabilities of possible outcomes of selecting boys and girls in a tree diagram.
3. Find the probability of selecting both girls.
4. By how much the probability of getting at least one boy is less than the total probability? Calculate it.

The monthly consumption of electricity (in units) of 50 consumers is given in the table below.

1. Write the formula to find the median of a continuous series.
2. Find the modal class and median class of the given data.
3. Calculate the median of the given data.
4. Did you find the modal class and median class same from the above computation? Are they always same? Give reason.

The weight of 20 students is presented here in the table.

1. In a continuous series, what does m represent in the formula ($\rm\overline X$)=$\rm \frac {\sum fm}{N}$ to calculate mean? Write it. 
2. Find the median class of the given data.
3. Calculate the average weight from the given data.
4. Is the class of measure of central tendencies of the given data same? Justify it. 

There are 1 red, 1 black and 1 white ball of the same shape and size in a bag. Two balls are drawn randomly one after another without replacement.

1. If A and B are two independent events, write the formula of P(A $\rm \cap$ B).
2. Show the probability of all the possible outcomes in a probability tree diagram. 
3. Find the probability of getting a red ball and a black ball. 
4. Is there any possibility of getting both balls of the same color? Give reason.

Which of the following statistical methods is not a measure of central tendency?

If a coin is tossed n times, what is its sample space?