An urn initially contains 3 red balls and 2 blue balls. You draw two balls without replacement. If both balls are the same color, you stop. If they are different colors, you put both balls back into the urn, add one additional red ball to the urn, and then draw two more balls. What is the probability that you do not stop on the first draw, but you stop on the second draw?
Show answer & explanation
Correct answer: B
Explanation
3 red, 2 blue total ways = 5C2 = 10
Ways to choose different colors = 3 × 2 = 6
Probability of not stopping the first time = 6/10 = 3/5
4 red, 2 blue total balls = 6
Probability of both red = 4C2 / 6C2 = 6/15
Probability of both blue = 2C2 / 6C2 = 1/15
Total probability = 6/15 + 1/15 = 7/15
Total desired probability = (3/5) × (7/15)
= 21/75 = 7/25