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Chapter 7: Problem 40

Electricity in the United States is generated from many sources. The following table gives the sources as well as their share in the production of electricity: $$ \begin{array}{lcccccc} \hline \text { Source } & \text { Coal } & \text { Nuclear } & \text { Natural gas } & \text { Hydropower } & \text { Oil } & \text { Other } \\ \hline \text { Share, } \% & 50.0 & 19.3 & 18.7 & 6.7 & 3.0 & 2.3 \\ \hline \end{array} $$ If a source for generating electricity is picked at random, what is the probability that it comes from a. Coal or natural gas? b. Nonnuclear sources?

Short Answer

Expert verified
The probability that a source for generating electricity picked at random comes from: a. Coal or natural gas is \(0.687\) or \(68.7\%\). b. Nonnuclear sources is \(0.807\) or \(80.7\%\).

Step by step solution

01

Calculate the probability of a source picked coming from coal or natural gas

To calculate the probability that a source picked at random comes from coal or natural gas, we simply add their shares and divide by 100. Probability = (Share of Coal + Share of Natural Gas) / 100 = (50.0 + 18.7) / 100 = 68.7 / 100
02

Calculate the probability of a source picked coming from nonnuclear sources

To calculate the probability that a source picked at random comes from nonnuclear sources, we subtract the share of nuclear sources from 100 and then divide by 100. Probability = (100 - Share of Nuclear) / 100 = (100 - 19.3) / 100 = 80.7 / 100
03

Simplify the probabilities

Now we need to simplify the probabilities found in Step 1 and Step 2. a. Probability of source picked coming from coal or natural gas: P(Coal or Natural Gas) = 68.7 / 100 = 0.687 b. Probability of source picked coming from nonnuclear sources: P(Nonnuclear sources) = 80.7 / 100 = 0.807 Thus, the probability that a source for generating electricity picked at random comes from: a. Coal or natural gas is 0.687 or 68.7%. b. Nonnuclear sources is 0.807 or 80.7%.

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