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Chapter 2: Q15E (page 65)

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?

Short Answer

Expert verified

a. Theprobability that at least two purchase an electric dryer is 0.572

b. The probability that at least one of each type is purchased is 0.879

Step by step solution

01

Given information

Five different customers at a certain store purchased two types of clothes dryer.

02

Compute the probability

a.

The probability that at most one of these purchases an electric dryer is 0.428.

The probability that at least two purchase an electric dryer is computed as,

\(\begin{aligned}1 - P\left( {atmost\;one\;of{\rm{ }}these{\rm{ }}purchases{\rm{ }}an{\rm{ }}electric{\rm{ }}dryer} \right) &= 1 - 0.428\\ &= 0.572\end{aligned}\)

Therefore, the probability that at least two purchase an electric dryer is 0.572.

b.

The probability that all five purchase gas is 0.116.

The probability that all five purchase electric is 0.005.

The probability that at least one of each type is purchased is computed as,

\(\begin{aligned}P\left( {atleast\;one\;of\,each\;type} \right) &= 1 - \left( {P\left( {all\;five\;purchase\;gas} \right) + P\left( {all\;five\;purchase\;electric} \right)} \right)\\ &= 1 - \left( {0.116 + 0.005} \right)\\ &= 0.879\end{aligned}\)

Therefore, the probability that at least one of each type is purchased is 0.879.

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