A venture capitalist invests in startup technology companies. She expects about 10% of these companies to be successful.

(a) What is the probability that she will have to invest in more than four companies before she comes upon one that is successful? Be sure to state any assumptions you make.

(b) Explain why a binomial random variable is not appropriate for calculating the answer in part (a).

(c) How many companies should she expect to have to invest in before she comes upon one that is successful? [For 0 < p ≤ 1, p {1 + 2(1 – p) + 3(1 – p)² + …) = 1/p]