GCSE Maths Probability questions by topic

One die, two questions.

1. (a)A fair six-sided die is rolled once. Write P(six) as a fraction.[2]
2. (b)Write P(not six).[2]

Drawing from a bag with replacement.

1. (a)A bag holds 5 red and 3 blue counters. One is drawn at random and replaced, 120 times in total. Write P(red).[2]
2. (b)How many red counters would you expect in the 120 draws?[2]

Weather that cannot overlap.

1. (a)On a day in March, P(rain) = 0.3 and P(snow) = 0.05, and both cannot fall together. Find P(rain or snow).[2]
2. (b)Find P(neither rain nor snow).[2]

A suspicious die.

1. (a)A die is rolled 300 times and lands on six 42 times. Calculate the relative frequency of rolling a six.[2]
2. (b)The theoretical probability is 1⁄6. What does the comparison suggest about the die?[2]

A shaded spinner is spun.

1. (a)A spinner has 10 equal sectors and 4 are shaded. Write down P(shaded).[1]
2. (b)Write down P(not shaded).[1]
3. (c)The spinner is spun 200 times. Work out the expected number of shaded results.[2]

A two-way table splits two year groups.

1. (a)Of 45 pupils, 24 are in Year 10 and the rest in Year 11; 27 pupils play sport, of whom 16 are in Year 10. Work out how many Year 11 pupils play sport.[1]
2. (b)A pupil is chosen at random. Work out P(plays sport).[2]
3. (c)Work out P(in Year 10).[1]

A frequency tree.

1. (a)Of 80 pupils, 3⁄5 are boys. ¼ of the boys wear glasses and 3⁄8 of the girls wear glasses. Copy and complete the frequency tree, giving all four final counts.[3]
2. (b)Find the probability that a pupil chosen at random wears glasses.[2]

Tea and coffee.

1. (a)Of 40 people, 25 drink tea, 20 drink coffee and 11 drink both. Draw or describe the Venn diagram with all four region counts.[3]
2. (b)Find the probability that a person chosen at random drinks neither.[2]

A two-way table.

1. (a)Of 100 adults, 60 are women, of whom 35 drive; the 40 men include 30 drivers. Find P(driver).[2]
2. (b)Find P(woman and driver).[2]
3. (c)State one conclusion the table supports about men and driving in this sample.[1]

Conditional from a table. (Higher)

1. (a)Using the same table (60 women with 35 drivers, 40 men with 30 drivers), find P(driver).[2]
2. (b)Find P(driver | woman), giving your answer as a fraction in its simplest form.[3]

Two beads leave a bag without replacement.

1. (a)A bag holds 4 red and 5 blue beads. Two are drawn without replacement. Write the four probabilities on the branches of a tree.[2]
2. (b)Work out P(both red).[2]
3. (c)Work out P(at least one red).[1]

Two counters, no replacement. (Higher)

1. (a)A bag holds 5 red and 4 blue counters. Two are drawn without replacement. Find P(red, red).[2]
2. (b)Find P(red, blue).[2]
3. (c)Find P(exactly one red).[2]

With or without replacement. (Higher)

1. (a)A box holds 3 toffees and 7 chocolates. Two sweets are picked with replacement. Find P(both toffees).[2]
2. (b)The picks are now without replacement. Find P(both toffees), as a fraction in simplest form.[2]
3. (c)Explain why replacing the first sweet raises the chance of two toffees.[2]

Set notation on 1 to 20. (Higher)

1. (a)The universal set ξ is the integers 1 to 20. A is the set of multiples of 3 and B is the set of even numbers. List A ∩ B.[2]
2. (b)Find n(A) and n(A ∪ B).[3]
3. (c)Find n((A ∪ B)′).[1]

Parcels and damage. (Higher)

1. (a)A courier delivers parcels: 0.7 arrive on time, and on-time parcels are undamaged with probability 0.9, while late parcels are undamaged with probability 0.75. Copy and complete the tree diagram.[2]
2. (b)Find P(on time and undamaged).[2]
3. (c)Find P(undamaged).[2]

Set notation over 1 to 15. (Higher)

1. (a)The universal set is the integers 1 to 15. Set A is the multiples of 3 and set B is the even numbers. List A ∩ B.[2]
2. (b)Work out n(A ∪ B).[2]
3. (c)Work out n((A ∪ B)′).[1]

A factory mixes two machine types. (Higher)

1. (a)60% of machines are type X, which are faulty 5% of the time; the rest are type Y, faulty 2% of the time. Copy and complete a tree diagram.[2]
2. (b)Work out the probability that a randomly chosen machine is faulty.[3]
3. (c)Given a machine is faulty, work out the probability it is type X.[1]

A suspicious die is rolled again. (Higher)

1. (a)A die lands six 100 times in 600 rolls. Work out the relative frequency of a six.[2]
2. (b)Explain why this evidence alone does not prove the die is fair.[2]
3. (c)A second batch of 600 rolls lands 130 sixes. Work out the combined relative frequency, to 3 significant figures.[2]