Handling Data 5

3 marks · Normal

A spinner has three equal sectors labelled A, B, and C. The spinner is spun twice. Draw a tree diagram and calculate the probability that:

(a)

Both spins result in the letter B.

[1 mark]

(b)

At least one spin shows the letter C.

[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) 1/9

(b) 5/9 · must show Complementary method or direct counting of cases

Must show: Tree diagram with branches labelled and probabilities shown

Common mistakes: Forgetting to use 'at least one' method (using 1-P(None))

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Correctly identifies probability for BB as (1/3) × (1/3).

M2 (b) · 1 mark · Finds P(no C): (2/3) × (2/3) = 4/9, then uses 1 – 4/9.

A1 (b) · 1 mark · Gives final answer 5/9 for (b).

Worked solution

Tree diagram branches: 1st spin: A, B, C with 1/3 each. For each, 2nd spin: A, B, C with 1/3 each.

(a): P(B and B) = 1/3 × 1/3 = 1/9

(b): Find P(no C in both spins) = 2/3 × 2/3 = 4/9

So, P(at least one C) = 1 − 4/9 = 5/9