Mail Delivery A local postal carrier distributes

Chapter 4, Problem 18E

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QUESTION:

A local postal carrier distributes first-class letters, advertisements, and magazines. For a certain day, she distributed the following numbers of each type of item.

\(\begin{array}{lcrc} \text { Delivered to } & \begin{array}{c} \text { First-class } \\ \text { letters } \end{array} & \text { Ads } & \text { Magazines } \\ \hline \text { Home } & 325 & 406 & 203 \\ \text { Business } & 732 & 1021 & 97 \end{array}\)

If an item of mail is selected at random, find these probabilities.

a. The item went to a home.

b. The item was an ad, or it went to a business.

c. The item was a first-class letter, or it went to a home.

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QUESTION:

A local postal carrier distributes first-class letters, advertisements, and magazines. For a certain day, she distributed the following numbers of each type of item.

\(\begin{array}{lcrc} \text { Delivered to } & \begin{array}{c} \text { First-class } \\ \text { letters } \end{array} & \text { Ads } & \text { Magazines } \\ \hline \text { Home } & 325 & 406 & 203 \\ \text { Business } & 732 & 1021 & 97 \end{array}\)

If an item of mail is selected at random, find these probabilities.

a. The item went to a home.

b. The item was an ad, or it went to a business.

c. The item was a first-class letter, or it went to a home.

ANSWER:

Step 1 of 3

a) Consider,

\(\begin{array}{|c|c|c|c|c|} \hline \text { Delivered to } & \text { First-class letters } & \text { Ads } & \text { Magazines } & \text { Total } \\ \hline \text { Home } & 325 & 406 & 203 & 934 \\ \hline \text { Business } & 732 & 1021 & 97 & 1850 \\ \hline \text { Total } & 1057 & 1427 & 300 & 2784 \\ \hline \end{array}\)

The probability that the item went to a home is:

\(\begin{aligned} P(\text { item went to a home }) & =\frac{(325+406+203)}{2784} \\ & =0.3354 \end{aligned}\)

Therefore, The probability that the item went to a home is 0.3354.

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