Handling Data 2

5 marks · Hard

In a board game, two fair eight-sided dice are thrown, one after the other. Each die is numbered from 1 to 8.

(a)

List all the possible outcomes if the order is important for the combination (show your working).

[2 marks]

(b)

What is the probability that both dice show the same number?

[1 mark]

(c)

Calculate the probability that the sum of the two dice is 10.

[2 marks]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) 64 outcomes

(b) 1/8

Common mistakes: Not considering order; Incorrect number of total outcomes; Arithmetic errors

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Gives number of possible outcomes as 8×8 = 64 (shows working).

A1 (a) · 1 mark · Explains that ordinal pairs (a,b) where 1≤a≤8, 1≤b≤8, total 64 ordered pairs. (follow-through)

M1 (b) · 1 mark · There are 8 possible pairs where dice show same value out of 64.

M1 (c) · 1 mark · Lists all ordered pairs that sum to 10.

A1 (c) · 1 mark · Correctly calculates probability as 7 out of 64. (follow-through)

Worked solution

a) Each die has 8 outcomes, so total ordered possible outcomes = 8 × 8 = 64. List could be (1,1), (1,2),...,(8,8).

b) Both dice show same: (1,1), (2,2), ..., (8,8): 8 possibilities. Probability = 8/64 = 1/8.

c) Sum is 10: Possible ordered pairs: (2,8), (3,7), (4,6), (5,5), (6,4), (7,3), (8,2): total 7 pairs. Probability = 7/64.