IGCSE Maths Probability topical questions

A bag holds 9 counters: 4 white, 3 black and 2 grey. One counter is drawn.

1. (a)Write down P(white).[1]
2. (b)Find P(not white).[1]
3. (c)Find P(black or grey).[2]

A spinner wins with probability 0.3. It is spun 80 times.

1. (a)Calculate the expected number of wins.[2]
2. (b)The spinner actually wins 27 times. Comment on whether the spinner appears fair.[2]

Two fair coins are flipped and the score is 2 points for two heads, 1 point for exactly one head and 0 points for no heads.

1. (a)List the four outcomes of the sample space.[1]
2. (b)Find P(score = 1).[2]
3. (c)Find the expected score over 40 games.[2]

Two fair dice are rolled and their scores added.

1. (a)Write down the total number of outcomes.[1]
2. (b)Find P(total = 7).[2]
3. (c)Find P(total greater than 9).[2]

A bag contains counters such that P(red) = 0.4. A counter is drawn, replaced, and a second counter is drawn.

1. (a)Find P(both counters are red).[2]
2. (b)Find P(exactly one of the two counters is red).[3]

Of 40 people, 25 like tea, 20 like coffee and 10 like both.

1. (a)Complete the Venn diagram: find the number who like only tea, only coffee, both, and neither.[3]
2. (b)One person is chosen at random. Find P(neither).[2]

A machine passes each item with probability 0.9. Two items are checked independently.

1. (a)Write down the four branch probabilities of the tree diagram.[2]
2. (b)Find P(both items pass).[1]
3. (c)Find P(at least one item fails).[2]
4. (d)In 500 independent pairs of items, find the expected number of pairs containing a failure.[1]

A box holds 7 lemon and 3 mint sweets. Two sweets are eaten without replacement.

1. (a)Find P(both sweets are lemon).[2]
2. (b)Find P(one sweet of each flavour).[3]
3. (c)Hence write down P(the two sweets are the same flavour).[1]

A bag holds 5 red and 4 blue counters. Two counters are drawn without replacement. (Extended)

1. (a)Write the probabilities on the branches of a tree diagram for the two draws.[1]
2. (b)Find P(both red).[2]
3. (c)Find P(the two counters have different colours).[2]

Of 60 runners, 35 drink water during training and 25 drink a sports drink. 38 runners finished a race in under 30 minutes; 28 of these drank water. (Extended)

1. (a)Complete the two-way table (water / sports drink against under 30 min / 30 min or over).[2]
2. (b)One runner is chosen at random. Find P(finished in under 30 minutes).[2]
3. (c)Given that a runner finished in under 30 minutes, find the probability that they drank water.[2]

An archer hits the target with probability 0.85 on each shot. Three shots are fired independently. (Extended)

1. (a)Write down P(miss on one shot).[1]
2. (b)Find P(all three shots miss).[2]
3. (c)Find P(at least one hit), giving your answer to 3 significant figures.[3]

Of 90 shoppers, 40 are loyalty members. 30 members and 24 non-members buy own-brand products. (Extended)

1. (a)Complete the two-way table (member / non-member against own-brand / not own-brand).[2]
2. (b)One shopper is chosen at random. Find P(member).[1]
3. (c)Given that a shopper is a member, find P(buys own-brand).[2]
4. (d)Given that a shopper buys own-brand, find P(member).[1]

A bag holds 5 red and 3 green sweets. Two sweets are taken without replacement. (Extended)

1. (a)Write down the four branch probabilities of the tree diagram.[2]
2. (b)Find P(the two sweets have different colours).[2]
3. (c)Given that the two sweets have different colours, find P(the first sweet was red).[3]

A striker scores on 71 of 250 penalty attempts. (Extended)

1. (a)Estimate P(scores) as a decimal.[2]
2. (b)Find the expected number of goals in 40 attempts.[2]
3. (c)Explain why the expected number need not be a whole number.[2]
4. (d)A journalist claims “more than 11 goals” in 40 attempts. Is the claim supported by the expectation?[1]