Question

1a) In a certain year, 89% of all Caucasians in the U.S., 75% of all African-Americans, 75% of all Hispanics, and 74% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 64% Caucasian, 11% African-American, and 14% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic? (Round your answer to the nearest whole percent.)

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1b)According to a study in a medical journal, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that men who were very active (burning about 3,500 calories daily) were a fifth as likely to develop diabetes compared with men who were sedentary. Assume that one in 12 middle-aged men is very active, and the rest are classified as sedentary. What is the probability that a middle-aged man with diabetes is very active? (Round your answer to four decimal places.)

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Answer 1

Problem 1(a)

Suppose, there are number of US residents.

Then, number of Hispanics

Now, among those Hispanics, only of them use the Internet for email.

i.e.,

Therefore, percentage of Hispanic U.S. residents who used the Internet for e-mail

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Problem 1(b)

Let be the event that a middle aged man is very active.

Let be the event that a middle aged man has diabetes.

According to the medical journal, of a sample of middle-aged men had developed diabetes.

i.e.,

Next, we are assuming that one in middle-aged men is very active, i.e.,

Next, we have a conditional probability statement which says if a man is active, then he is a fifth as likely to develop diabetes.

i.e.,

We want to compute the conditional probability of a middle-aged man having diabetes if he is very active.

i.e.,

We will simply follow the definitions of conditional probability and use all the information that is given to us.

We have,