Probability without replacement

Question

1.A jar contains 4 red balls and 7 blue balls. Two balls are drawn at random from the jar without replacement. What is the probability that exactly one of the balls is red.

2. A jar contains 5 red balls and 12 blue balls. Two balls are drawn at random from the jar without replacement. What is the probability that both balls are red.

Answer 1

1. So for this we want to either get a red ball on the first pull or a red ball on the second, not both. So to solve this let's find the probability of the first scenario then add the second scenario: 4/11 * 7/10 + 7/11 * 4/10=50.9%
2. Now we want both balls to be red so let's find the probability of that happening: 5/17*4/16=7.35%