Question

A local bakery estimates that 25% of its customers purchase chocolate croissants. Each customer is only allowed to purchase one chocolate croissant per day.

a. In a random sample of 9 customers, what is the probability that at least five will purchase a chocolate croissant.

b. In a random sample of 12 customers what is the probability that two or less do not purchase a chocolate croissant.

c. If on a particular day, the bakery makes only 35 chocolate croissants, and 180 customers come to the shop, what is the approximate probability that at least one customer who wants a chocolate croissant will not be able to purchase one?

Answer 1

a)

Let X denote the croissants purchased. Then

Required probability =

b)

Let X denote the number of cutomers who do not purchase croissant.

Then

Required probability =

c)

Let X denote the number of cutomers who do not purchase croissant.

Then

Required probability = P(at least one customer who wants a chocolate croissant will not be able to purchase one)

= 1 - P(no customer who wants a chocolate croissant will not be able to purchase one)