# Homework 8

Due Tuesday, November 22:

Section 7.3 #24

Section 8.1 #6, 40, 41, 51

Do the following problem as well:

A wealthy venture capitalist is looking to invest in many tech startups. He considers them all “long shots” and therefore wants to invest in many in order to get lucky at least once. He finds 30 different tech startups, each of which he considers to have a probability of becoming one billion dollar company within 5 years to be 1%. He then calculates that the probability that none of them become one billion dollar company is $(0.99)^{30}$, about 74%. He concludes that the probability that at least one of the startups becomes worth one billion dollars is about 26%.

Assume that the probability of each startup becoming worth one billion dollars within 5 years really is 1%. Do you agree or disagree with his assessment that the probability that at least one of them becoming worth one billion dollars must be about 26%?  Explain why or why not, and show what assumptions are needed to come to this conclusion.

The following exercises are optional and need not be turned in:

Section 8.1 #1, 4, 5, 7, 13, 16, 17

Section 8.2 #3-8, 15-17