Algorithms and Analysis

Probability

1. Consider a jar with white and black balls, where the number of black balls is even. We are given that the probability that two balls, picked at random from the jar, are both white is 1/2 . Calculate the minimum number of balls in the jar.

2. Suppose there are A black balls and B white balls in a jar. We randomly pick a ball from the jar and put it back until we have a white ball. Denote X as the number of balls we have picked. What would be the distribution and expectation of X? (The distribution is the general formula for P(x = k) for each k N). (You should derive the expectation from the definition)