Handling Data 5
4 marks · NormalA bag contains 3 yellow marbles and 2 green marbles. One marble is picked at random, replaced, and then another is picked. Answer the following:
Write down the probability of picking a yellow marble both times.
Write down the probability of picking a green marble first and a yellow marble second.
Find the probability that the two marbles are of different colours.
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) 9/25
(b) 6/25
(c) 12/25 · must show Adds probability of (yellow then green) and (green then yellow)
Common mistakes: Forgetting to sum both possible orders in part (c)
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Identifies probability for two yellows as (3/5) × (3/5).
M2 (b) · 1 mark · Multiplies correct probabilities for green then yellow (2/5 × 3/5).
M3 (c) · 1 mark · Finds probability for yellow then green (3/5 × 2/5) and green then yellow (2/5 × 3/5).
A1 (c) · 1 mark · Sums both probabilities to get 12/25.
Worked solution
(a) P(yellow both times) = 3/5 × 3/5 = 9/25
(b) P(green then yellow) = 2/5 × 3/5 = 6/25
(c) P(different colours) = (3/5 × 2/5) + (2/5 × 3/5) = 6/25 + 6/25 = 12/25