What is the probability of drawing blue then red without replacement from a bag containing 3 red and 2 blue balls?

• A. 3/10
• B. 1/5
• C. 2/5
• D. 1/2

Answer: (A)

When drawing without replacement, the outcome of the first draw affects the second, so you multiply the probabilities of the sequential steps.

First, draw blue: there are 2 blue out of 5 total, so the chance is 2/5. After taking a blue ball, there are 3 red and 1 blue left, a total of 4 balls. The chance the next ball is red is then 3/4. Multiply the two probabilities: (2/5) × (3/4) = 6/20 = 3/10.

So the probability of blue first and then red is 3/10.