There is a frozen custard machine in the St. Louis airport that dispenses strawberry con- cretes randomly with probability and chocolate concretes otherwise.¹ (a) You are traveling with 6 other people and buy a concrete for everyone in the group, including yourself. What is the probability that 4 of you will get chocolate? (b) If 2 of you want strawberry would you expect to get enough strawberry for both of

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(4) There is a frozen custard machine in the St. Louis airport that dispenses strawberry concretes randomly with probability \(\frac{4}{15}\) and chocolate concretes otherwise.

(a) You are traveling with 6 other people and buy a concrete for everyone in the group, including yourself. What is the probability that 4 of you will get chocolate?

(b) If 2 of you want strawberry, would you expect to get enough strawberry for both of those 2 people? Why?
Transcribed Image Text:(4) There is a frozen custard machine in the St. Louis airport that dispenses strawberry concretes randomly with probability \(\frac{4}{15}\) and chocolate concretes otherwise. (a) You are traveling with 6 other people and buy a concrete for everyone in the group, including yourself. What is the probability that 4 of you will get chocolate? (b) If 2 of you want strawberry, would you expect to get enough strawberry for both of those 2 people? Why?
Expert Solution
Step 1

From the given information,

The probability of strawberry concrete is 4/15.

The probability of chocolate concrete is 1-415=1115.

a)

Given that you are traveling with 6 other people and buy a concrete for everyone in the group, including yourself.

That is, the total number of people is6+1=7.

Let X be the number of people will get chocolate concrete follows binomial distribution with n=7 and p=Pchocolate concrete=1115.

The PMF for X is,

PX=x=nxpx1-pn-x               =7x1115x1-11157-x, x=0,1,2,...,7

The probability that 4 of you will get chocolate is,

PX=4=74111541-11157-4              =7!4!7-4!111544153             =0.192

 

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