Handling Data 7

4 marks · Normal

You roll a fair six-sided die twice.

(a)

Write down the probability of getting a 2 on the first roll and a 4 on the second roll.

[1 mark]

(b)

Find the probability of getting an even number on both rolls.

[2 marks]

(c)

Calculate the probability of getting at least one 6 in the two rolls.

[1 mark]

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) 1/36

(b) 1/4

Must show: Correct multiplication for each part, At least one (complement method acceptable)

Common mistakes: Not using multiplication; Not using complement for at least one

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Writes down probability of 2 then 4: 1/6 × 1/6 = 1/36.

M1 (b) · 1 mark · Finds probability of even on one roll is 3/6 = 1/2; both rolls: (1/2)×(1/2).

A1 (b) · 1 mark · Gives correct answer: 1/2 × 1/2 = 1/4.

M2 (c) · 1 mark · Uses complementary probability: 1 - P(no 6s) = 1 - (5/6 × 5/6) = 11/36.

Worked solution

a) P(2 then 4) = P(2 on first) × P(4 on second) = 1/6 × 1/6 = 1/36.

b) Even numbers on a die are 2, 4, 6: P(even) = 3/6 = 1/2. Both rolls: 1/2 × 1/2 = 1/4.

c) P(no 6 on a roll) = 5/6. Both rolls no 6: 5/6 × 5/6 = 25/36. So P(at least one 6) = 1 - 25/36 = 11/36.