Free Year 9 Two-way tables Practice | Skillo

Question 1 — Easy

Priya has a bag containing 3 green cards and 2 yellow cards. She draws one card, records its colour, and puts it back before drawing a second card. What is the probability that both cards drawn are green?

Answer: Because the draw is with replacement, the sample space for each draw is identical: P(green) = 3/5 each time. The probability of both being green is 3/5 × 3/5 = 9/25. Option A is just P(green) for one draw, B mistakes the numerator as 6 (adding instead of multiplying), and D uses 3/5 × 1/2 incorrectly.

Question 2 — Medium

Anika has a bag containing 4 green marbles and 3 yellow marbles. She picks one marble, records its colour, and puts it back before picking a second marble. What is the probability that both marbles are green?

Answer: Since the marble is replaced, each pick is independent. P(green on first pick) = 4/7 and P(green on second pick) = 4/7. P(both green) = 4/7 × 4/7 = 16/49. Option A uses 2/7 × 4/7, confusing the number of yellow marbles with the probability. Option C multiplies 4/7 × 3/7, using the probability of yellow instead of green for the second pick. Option D gives the probability of a single green pick, ignoring the compound event.

Question 3 — Hard

A box contains 4 red and 3 blue marbles. Kofi draws one marble and does not replace it before drawing a second. What is the probability that the first marble is red and the second marble is blue?

Answer: Without replacement, P(red first) = 4/7 and P(blue second | red first) = 3/6 = 1/2. The compound probability is 4/7 × 1/2 = 4/14 = 2/7. Option A uses the with-replacement denominator (7 × 7 = 49): 4/7 × 3/7 = 12/49. Option C is the unsimplified product 12/42, which equals 2/7 but has not been simplified — this is a partially correct response. Option D is just P(red) × P(blue) added rather than multiplied.