Answer to Question #236313 in Statistics and Probability for Jack

Question

Suppose that two types of cloth dryers namely, gas or electric dryer are available in a store. Suppose seven students visited that store and purchased each of the electric or gas dryer.

a. If the probability that at most two of the students purchase an electric dryer is 0.333,

what is the probability that at least three of them will purchase an electric dryer?

b. If the probability that at least five of them purchase a gas dryer is 0.114, what is the

probability that at most four of them purchase a gas dryer?

c. If the probability that at least one of them purchase a gas dryer is 0.006, what is the

probability that none of them will purchase a gas dryer?

d. If the probability that all the seven students purchase a gas dryer is 0.211 and

probability that all of them purchases an electric dryer is 0.413,

i. what is the probability that all purchases same type of dryer? and

ii. what is the probability that at least one of each type of dryer is purchased?

Answer 1

Let $X=$ the number of students who will purchase an electric dryer.

Let $Y=$ the number of students who will purchase an gas dryer

a.

$$P(X\geq3)=1-P(X\leq2)=1-0.333=0.667$$

The probability that at least three of students will purchase an electric dryer is $0.667.$

b.

$$P(Y\leq4)=1-P(Y\geq5)=1-0.114=0.886$$

The probability that at most four of them will purchase a gas dryer is $0.886.$

c.

$$P(Y=0)=1-P(Y\geq1)=1-0.006=0.994$$

The probability that none of them will purchase a gas dryer is $0.994.$

d.

i.

$$P((X=7)\cup (Y=7))=P(X=7)+P(Y=7)-$$

$$=P(X=7)+P(Y=7)-P((X=7)\cup (Y=7))$$

$$=0.211+0.413-0=0.624$$

The probability that all purchases same type of dryer is $0.624.$

ii.

$$1-0.624=0.376$$

The probability that at least one of each type of dryer is purchased is $0.376.$