if you were to select 15 boxes at random, what is the probability that exactly 8 of the 15 would weigh 24 ounces?

Question

A store sells old-time assorted candies in four different size boxes, by weight in ounces. The following model describes the probability of purchasing each size for a random customer who buys this kind of candy.

Weight- 12 16 24 36

Probability- .05 .45 .35 . 15

Answer 1

You should be able to do this as a binomial expansion

Lets call x the probabilty of choosing a 24 oz box (.35) and

y the probability of not choosing a 24 oz box (.65)

In the binomial expansion of (x+y)^15 we would be interested in the term x^8y^7

The coefficient for this term is 6435 so probability is

(6435)(.35)^8(.65)^7= .071