According to Consumer Digest (July/August 1996), the....

According to Consumer Digest (July/August 1996), the. probable location of personal computers $(\mathrm{PC})$ in the home is as follows: Adult bedroom: 0.03 Child bedroom: 0.15 Other bedroom: 0.14 $\begin{array}{cc}\text { Office or den: } & 0.40\end{array}$ Other rooms: 0.28 (a) What is the probability that a $\mathrm{PC}$ is in a bedroom? (b) What is the probability that it is not in a bedroom? (c) Suppose a household is selected at random from households with a $\mathrm{PC}$; in what room would you expect to find a $\mathrm{PC} ?$

According to Consumer Digest (July/August
1996), the. probable location of personal computers $(\mathrm{PC})$ in the home is as follows:
Adult bedroom: 0.03 Child bedroom: 0.15 Other bedroom: 0.14 $\begin{array}{cc}\text { Office or den: } & 0.40\end{array}$
Other rooms:
0.28
(a) What is the probability that a $\mathrm{PC}$ is in a bedroom?
(b) What is the probability that it is not in a bedroom?
(c) Suppose a household is selected at random from households with a $\mathrm{PC}$; in what room would you expect to find a $\mathrm{PC} ?$

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Key Concepts

Probability Distribution

A probability distribution assigns likelihoods to different outcomes for a random variable. In this context, it represents the probabilities associated with various household locations where a PC might be found, allowing for an overall picture of how PCs are distributed in homes.

Expected Value and Mode

The expected value typically refers to the average outcome when considering all probabilities of a distribution. However, when selecting the most likely single outcome from a set of discrete options, the mode—the outcome with the highest probability—is used to identify the most typical or expected location.

Addition Rule in Probability

The addition rule for probability states that if you have mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities. This concept is used when combining probabilities across disjoint outcomes, such as the different types of bedrooms where a PC might be located.

Complement Rule

The complement rule states that the probability of an event not occurring is equal to one minus the probability of that event occurring. This principle is applied to determine the probability of a PC not being in a bedroom when the probability of it being in a bedroom is known.

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