Sec 4 E-Math Probability topical questions

A fair coin is flipped once. Write down P(heads).

A fair die is rolled once. Find P(a number greater than 4).

A bag holds 3 red, 4 blue and 5 green counters. One counter is drawn at random. Find P(not blue).

From the same bag (3 red, 4 blue, 5 green), find P(green or red).

Two fair coins are tossed. List the sample space and find P(two heads).

A bag holds 2 gold, 3 silver and 5 bronze medals, identical except for colour. One medal is drawn at random. Find (a) P(gold) and (b) P(not silver).

A fair die is rolled twice. List all the outcomes giving a sum of 5, and find P(sum is 5).

Two fair dice are rolled and the sum recorded. (a) Explain why there are 36 equally likely outcomes. (b) Find P(the sum is 8). (c) Find P(the sum is less than 4 or more than 10).

1. (a)Why 36.[1]
2. (b)P(sum is 8).[2]
3. (c)P(sum < 4 or sum > 10).[2]

A packet holds 4 strawberry and 3 mint sweets. Two sweets are eaten one after the other. (a) Copy and complete a tree diagram for the two draws. (b) Find P(the two sweets have the same flavour).

1. (a)Tree diagram.[2]
2. (b)P(same flavour).[2]

Two fair dice are rolled. Find P(the sum is a prime number).

A fair coin is tossed three times. (a) Find P(exactly two heads). (b) Find P(at least one head).

1. (a)Exactly two heads.[2]
2. (b)At least one head.[2]

Each child in a family is equally likely to be a boy or a girl, independently. The family has two children. Find the probability that at least one is a girl.

A toolbox holds 5 screwdrivers and 3 hammers. Two tools are drawn at random, one after the other, without replacement. (a) Write the probabilities on the branches of a tree diagram. (b) Find P(both tools are hammers).

At a café, 70% of customers order coffee and the rest order tea. Of the coffee drinkers, 60% add sugar; of the tea drinkers, 30% add sugar. Find (a) P(a customer orders coffee and adds sugar), (b) P(a customer orders tea and adds sugar), and (c) P(a customer adds sugar).

Events A and B satisfy P(A) = 1/3, P(B) = 1/4 and P(A and B) = 1/12. (a) Determine whether A and B are independent, showing your reasoning. (b) Find P(A or B).

1. (a)Independence test.[2]
2. (b)P(A or B).[2]

A bag holds some red counters and 8 blue counters. A counter is drawn at random and replaced; this is repeated many times. Given that P(red) = 3/5, find the number of red counters in the bag.

A box of 10 batteries contains 4 flat ones. Three batteries are taken at random, one after another, without replacement. (a) Find the probability that exactly one of the three is flat. (b) Find the probability that at least one is flat.

1. (a)Exactly one flat.[4]
2. (b)At least one flat.[2]

A spinner lands on "win" with probability 0.3. It is spun twice. (a) Draw the tree diagram. (b) Find P(exactly one win). (c) Find P(at least one win), giving your answer as a decimal.

1. (a)Tree diagram.[1]
2. (b)Exactly one win.[2]
3. (c)At least one win.[1]

A bag holds 4 red and 2 white counters. Two counters are drawn at random without replacement. (a) Draw a tree diagram with probabilities. (b) Find P(the two counters are the same colour). (c) Find P(the two counters are different colours).

1. (a)Tree diagram.[2]
2. (b)Same colour.[2]
3. (c)Different colours.[2]

Jack throws darts at a board; each throw hits the bullseye independently with probability 0.35. He throws three darts. (a) Find P(three bullseyes). (b) Find P(no bullseye). (c) Find P(at least one bullseye). (d) Explain why the probabilities of 0, 1, 2 and 3 bullseyes must add up to exactly 1.

1. (a)Three bullseyes.[1]
2. (b)No bullseye.[2]
3. (c)At least one.[2]
4. (d)Explain the total.[1]