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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) 5 .116 and P(all five purchase electric) 5 .005, what is the probability that at least one of each type is purchased?

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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

The probability of at least two purchasing an electric dryer is 0.572 and the probability of at least one type of purchase is 0.879.

probability:

The probability that at least one person will acquire an electric dryer[tex]=0.428[/tex]

The probability that at least two people will buy an electric dryer is high = 1 - Probability of at least one

I bought a dryer

[tex]= 1-0.428\\\\= 0.572[/tex]

P(all 5 for purchasing gas)[tex]=0.116[/tex]

P(all 5 electrical purchases) [tex]=0.005[/tex]

P(at least 1 of each type purchased) = 1 -(P(only 1 type is purchased))

[tex]=1-\text{[P(all five purchases of gas)+P(all five purchases of electricity)]}[/tex]

[tex]= 1-0.116-0.005\\\\= 1-0.121\\\\=0.879[/tex]

Therefore, the final answer is "0.572 and 0.879".

Find out more information about the gas here:

brainly.com/question/26354986

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