5.4 Geometric Distribution Suppose we have an experiment where we will repeat binomial trials until we get the FIRST success. We use “n” to denote the first trial that is successful. Say we were trying to roll a 3. What is the probability that it happens on the first roll? What is probability it comes on the second? What is probability it comes on the third? Geometric probability distribution P(n) = p(1− p)n−1 where n is the number of the trial on which the first success occurs, and p is the probability of success on each trial. Note: p must be the same for each trial. 1
µ = this is the trial on which we EXPECT the first success p
1− p
and σ =
p
Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 57% of all people who take the state bar exam pass. What is the probability Bob passes on his first attempt? His second? His third? What is probability he needs more than 3 attempts? What is the expected number of times he would take the test before he is successful?