Question

Brooke walks to the convenience store everyday and passes a hot dog vendor that has a
30% chance of saying “Hello” to her. After she buys the newspaper, she takes a different
route home and does not see the vendor again until the next day.
a) What is the probability that the vendor will
say “Hello” exactly three times in the next
two weeks?
b) What is the probability that the vendor will not
say “Hello” until the 10th day?

Answer 1

a) $P(X=3)=C_{14}^30.3^3(1-0.3)^{14-3}=0.1943.$

b) $P=(1-0.3)^9*0.3=0.0121.$