There lies a typo-error when typing the part (b) of this question, which have identified and sort out; here is the right question below.
Consider the type of clothes dryer (gas or electric) purchased by each of five different customers at a certain store. a. If the probability that at most one of these purchases an electric dryer is .428, what is the probability that at least two purchase an electric dryer? b. If P(all five purchase gas) .116 and P(all five purchase electric) .005, what is the probability that at least one of each type is purchased?
Answer:
a) 0.572
b) 0.879
Step-by-step explanation:
Given that:
there are two types of dryer.
Gas dryer
Electric dryer
So, from the question a. If the probability that at most one of these purchases an electric dryer is .428, what is the probability that at least two purchase an electric dryer
Let us represent M with the event that at most one purchase is an electric dryer
Let use M' (i.e complement of M) to represent the event that at least two purchase an electric dryer.
Then if P (M) = 0.428
P(M') = 1 - P(M)
P(M') = 1 - 0.428
P(M') = 0.572
∴ the probability that at least two purchase an electric dryer = 0.572
b)
If P(all five purchase gas) .116 and P(all five purchase electric) .005, what is the probability that at least one of each type is purchased?
Let N represent the event that all five purchases are gas dryer
Then P (N) = 0.116
Let Q represent the event that all five purchase are electric dryer
Then P(Q) = 0.005
So (N∪Q); which is read as (N union Q) is the event that only one type of dryer is purchased.
so P(N∪Q) = ( 0.116+ 0.005)
= 0.121
Then the complement of (N∪Q) ; i.e (N∪Q)' signifies the event that at least one of each type is purchased;
So, P(N∪Q)' = 1 - (N∪Q)
P(N∪Q)' = 1 - 0.121
P(N∪Q)' = 0.879
∴ the probability that at least one of each type is purchased = 0.879
