From a bag containing 3 red and 2 blue balls, what is the probability of drawing two red balls without replacement?

• A. 1/5
• B. 1/3
• C. 3/10
• D. 4/5

Answer: (C)

When drawing without replacement, the probability of two specific successive outcomes is found by multiplying the probability of the first outcome by the probability of the second outcome given the first occurred.

Here, the chance the first draw is red is 3 out of 5. If that happens, there are now 2 red and 3 total balls left, so the chance the second draw is red is 2 out of 4, which is 1/2. Multiply: (3/5) × (1/2) = 3/10.

As a quick check, consider unordered pairs: there are C(5,2) = 10 total pairs, and red-red pairs come from choosing 2 red balls from 3, which is C(3,2) = 3. So the probability is 3/10 as well.