A bag contains 5 red and 4 blue identical balls. Id two balls are selected at random from the bag, one after…

Analyze the question: A bag has 5 red and 4 blue balls, so 9 balls in total. Two balls are drawn one after the other with replacement. We want P(first is red AND second is blue).

Concept: With replacement, the bag is restored after the first draw, so the two draws are independent. For independent events:

P(A and B) = P(A) × P(B)

Solution:

• P(first is red) = 5/9
• After replacement, the bag still has 5 red and 4 blue, so P(second is blue) = 4/9

P(red then blue) = 5/9 × 4/9 = 20/81

Common mistakes to avoid:

• Using 4/8 for the second draw. That is for draws without replacement, which would give 5/9 × 4/8 = 5/18 (option B, a trap).
• Adding the probabilities instead of multiplying them.

Exam tip: Look for the words "with replacement". They mean the denominator stays the same for every draw. "AND" means multiply. "OR" means add.