A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after…

Analyze the question: There are 5 balls in total (2 white, 3 blue). Two balls are drawn one after the other with replacement, so the probabilities stay the same on both draws. We want the probability that the two balls are of different colours.

Concept: With replacement, the draws are independent, so we multiply probabilities along each path. "Different colours" can happen in two ways, and we add them:

• White first, then blue (WB)
• Blue first, then white (BW)

Solution:

• P(White) = 2/5
• P(Blue) = 3/5

P(WB) = 2/5 × 3/5 = 6/25

P(BW) = 3/5 × 2/5 = 6/25

P(different colours) = 6/25 + 6/25 = 12/25

Check: P(same colour) = (2/5)² + (3/5)² = 4/25 + 9/25 = 13/25, and 1 − 13/25 = 12/25. ✓

Answer: D. 12/25

Tip: For "different colours" questions with two draws, remember to count both orders (WB and BW). A common mistake is to calculate only one order and get 6/25. Also, check whether the question says "with replacement" or "without replacement". Without replacement, the answer would have been 2/5 × 3/4 × 2 = 3/5, which is option B, a trap option!