In: Statistics and Probability
Two buckets are lying on a table. Bucket #1 has five red and two yellow balls in it. Bucket #2 contains three red and four yellow balls. In all of the questions below, the buckets start with this composition.
a. Two balls are drawn at random from bucket #1. What is the probability that one is red and one is yellow?
b. One ball is drawn at random from bucket #1 and placed into bucket #2. One ball is then drawn from bucket #2. What is the probability that this ball is red?
c. Balls are drawn one by one from bucket #2 until a red ball is drawn. What is the probability that the first red ball is drawn on the third draw.