# Exam-style Questions: Probability

1. In the game of 'Soap', two fair dice, with the faces numbered 1 to 6, are thrown.

The total of the scores on the dice is the score for that turn. The player then moves the same number of places as their score.

For example, if (3,5) is thrown, the player moves on 8 places.

a) Khalid wants to land on the space marked "Albert Square". He is now on "Coronation Street" which is 6 spaces away.

By considering the possibility space (all possible outcomes), work out the probability that Khalid lands on "Albert Square" on his next turn.

(3 marks)

Caroline does not want to land on "Ramsey Street" which is 7 spaces away.

b) What is the probability that Caroline does not land on "Ramsey Street" on her next turn?

(2 marks)

You can only escape from "Cell Block H" if you score the same number on each dice. John is on "Cell Block H".

c) What is the probability that John escapes on his next turn?

(1 mark)

(Marks available: 6)

Answer outline and marking scheme for question: 1

a) 5/36

(3 marks)

b) 5/6

(2 marks)

c) 1/6

(1 mark)

(Marks available: 6)

2. In a class of 20 pupils, 11 have dark hair, 7 have fair hair and 2 have red hair.

Two pupils are chosen at random to collect the homework. What is the probability that they

a) both have fair hair

(3 marks)

b) each have hair of a different colour

(4 marks)

(Marks available: 7)

Answer outline and marking scheme for question: 2

a) 21/190

(3 marks)

b) 226/380

(4 marks)

(Marks available: 7)

3. A bag contains five discs that are numbered 1, 2, 3, 4 and 5.

Rachel takes a disc at random from the bag. She notes the number and puts the disc back.

She shakes the bag and picks again. She adds this number to the first number.

a) Complete the table to show all the possible totals.

(2 marks)

b) Find the probability that Rachel's total is

(i) 10 [1]

(ii) 1 [1]

(iii) 3 or 4

(4 marks)

(Marks available: 6)

Answer outline and marking scheme for question: 3

a)

(2 marks)

b) (i) 1/25 or 0.04 or 4%

(1 mark)

(ii) 0 or impossible

(1 mark)

(iii) 5/25 or 1/25 or 0.2 or 20%

(2 marks)

(Marks available: 6)

4. The Morgan family leave Manchester to catch the 12 noon ferry from Dover.

The probability that they will catch the ferry is 0.9.

The Collins family leaves Croydon to catch the same ferry.

The probability that they will catch the ferry is 0.8.

The two events are independent.

a) Find the probability that

(i) Both families will catch the ferry

(2 marks)

(ii) Neither will catch the ferry

(2 marks)

b) (i) Complete the cumulative frequency table below.

(1 mark)

 Time (t minutes) t ≤ 20 t ≤ 20 t ≤ 40 t ≤ 60 t ≤ 80 Number of families

(ii) On the grid below, draw the cumulative frequency diagram of the waiting times of the 80 families.

(2 marks)

(Marks available: 7)

Answer outline and marking scheme for question: 4

a) (i) 0.72

(ii) 0.02

b) (i) 4, 23, 53, 71, 80.

(ii) Correct plots at 20, 40, 60, 80, 100.

Curve or ruled joins (at least 4 points).

(Marks available: 7)

5. Anil has five bars of chocolate in a cupboard.

Three are Kit-Kats, one is a Mars bar and one is a Fudge bar.

He takes one at random on each weekday to eat at school.

a) Calculate the probability that the bar of chocolate will be a Kit-Kat on both Monday and Tuesday of that week.

(2 marks)

b) Calculate the probability that the bar of chocolate will be a Kit-Kat on Monday, Tuesday and Wednesday and a Mars bar on Thursday.

(2 marks)

c)) Calculate the probability that the bar of chocolate will not be a Kit-Kat on any two consecutive days in that school week.

(3 marks)

(Marks available: 7)

Answer outline and marking scheme for question: 5

a) 3/10

(2 marks)

b) 1/20

(2 marks)

c) 1/10

(3 marks)

(Marks available: 7)