A survey of 1,095 adults was asked, \"Do you enjoy shopping for clothing for you

Question

A survey of 1,095 adults was asked, "Do you enjoy shopping for clothing for yourself?" The results indicated that 51% of the females enjoyed shopping for clothing for themselves as compared to 43% of the males. Suppose that the results indicated that of 547 males, 237 answered yes. Of 548 females, 278 answered yes. Construct a contingency table to evaluate the probabilities. Complete parts (a) through (d). a. What is the probability that a respondent chosen at random enjoys shopping for clothing for himself or herself? (Round to three decimal places as needed.) b. What is the probability that a respondent chosen at random is a female and enjoys shopping for clothing for herself? (Round to three decimal places as needed.) c. What is the probability that a respondent chosen at random is a female or is a person who enjoys shopping for clothing? (Round to three decimal places as needed.) d. What is the probability that a respondent chosen at random is a male or a female? (Round to three decimal places as needed.) A survey of 1,095 adults was asked, "Do you enjoy shopping for clothing for yourself?" The results indicated that 51% of the females enjoyed shopping for clothing for themselves as compared to 43% of the males. Suppose that the results indicated that of 547 males, 237 answered yes. Of 548 females, 278 answered yes. Construct a contingency table to evaluate the probabilities. Complete parts (a) through (d). a. What is the probability that a respondent chosen at random enjoys shopping for clothing for himself or herself? (Round to three decimal places as needed.) b. What is the probability that a respondent chosen at random is a female and enjoys shopping for clothing for herself? (Round to three decimal places as needed.) c. What is the probability that a respondent chosen at random is a female or is a person who enjoys shopping for clothing? (Round to three decimal places as needed.) d. What is the probability that a respondent chosen at random is a male or a female? (Round to three decimal places as needed.) A survey of 1,095 adults was asked, "Do you enjoy shopping for clothing for yourself?" The results indicated that 51% of the females enjoyed shopping for clothing for themselves as compared to 43% of the males. Suppose that the results indicated that of 547 males, 237 answered yes. Of 548 females, 278 answered yes. Construct a contingency table to evaluate the probabilities. Complete parts (a) through (d). a. What is the probability that a respondent chosen at random enjoys shopping for clothing for himself or herself? (Round to three decimal places as needed.) b. What is the probability that a respondent chosen at random is a female and enjoys shopping for clothing for herself? (Round to three decimal places as needed.) c. What is the probability that a respondent chosen at random is a female or is a person who enjoys shopping for clothing? (Round to three decimal places as needed.) d. What is the probability that a respondent chosen at random is a male or a female? (Round to three decimal places as needed.)

Explanation / Answer

Consider the table:

Thus:

a)

P(enjoy) = 515/1095 = 0.470319635 [answer]

b)

P(enjoy and female) = 278/1095 = 0.253881279 [answer]

c)

P(female or enjoy) = (278+270+237)/1095 = 0.716894977 [answer]

d)

P(male or female) = (547+548)/1095 = 1 [answer, sure event!]

Male Female Totals Enjoy 237 278 515 Not Enjoy 310 270 580 547 548 1095

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