Question

4. Suppose your goal in life is to have 3 successful startups. Given that 90% of startups fail, would it be unusual if you had to launch 50 startups to finally meet your goal? Argue using statistical ideas based on random variables.

Answer 1

The probability that a startup will not fail = 1 - 0.9 = 0.1

Let X denotes the number of startups that need to be launched to get 3 successful startups.

X ~ Negative Binomial( r = 3, p = 0.1)

The probability mass function of X is

Now,

The probability that one had to launch 50 startups to finally have 3 successful startups

Since the probability is very small, we can say that the event is quite unusual.