A card is drawn from a pack of playing cards and a dice is thrown. Events A and B are as follows: 

A: 'Jack is drawn from the pack' & B: ‘ a one is thrown on the dice’.

1. Write down the values of P(A), P(B)
2. Write down the value of P(A and B).

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).

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