Homework SourseA survey of 1095 adults was asked Do you enjoy shopping for
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.)
Solution
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 |
![A survey of 1,095 adults was asked, \](/WebImages/27/a-survey-of-1095-adults-was-asked-do-you-enjoy-shopping-for-1070932-1761560956-0.webp "A survey of 1,095 adults was asked, \")
