Question

In basketball, no number 16 seed beat a number 1 seed in 132 games. Use this to estimate p, the prob that a number 16 team beats a number 1 seed. Assume the outcomes of 16/1 seed games are iid Bernoulli(p)

Answer 1

Let p be the probability that number 16 seed beats number 1. Then probability that no number 16 seed beat a number 1 seed in 132 games =(1-p)132 . Now if this event has occured then we can estimate p by being 95% sure of this event.

So p132 = 0.95

132 ln(1-p) = ln(0.95)

ln(1-p) = ln(0.95)/132

1-p 0.9996

p 0.0004