A sample of 500 purchasing managers was selected across Australia to determine information concerning buying behaviour. Among the questions asked was, ‘Do you enjoy your role in the organisation?’ Of 240 males, 136 answered YES. Of 260 females, 224 answered YES.a. Construct a contingency tableb. What is the probability that a respondent chosen at random enjoys his/her role in the organisation?c. What is the probability that a respondent chosen at random is a female and enjoys her role in the organisation?d. What is the probability that a respondent chosen at random is a female or enjoys her/his role in the organisation?e. What is the probability that a respondent chosen at random is a male or a female?
Question
A sample of 500 purchasing managers was selected across Australia to determine information concerning buying behaviour. Among the questions asked was, ‘Do you enjoy your role in the organisation?’ Of 240 males, 136 answered YES. Of 260 females, 224 answered YES.a. Construct a contingency tableb. What is the probability that a respondent chosen at random enjoys his/her role in the organisation?c. What is the probability that a respondent chosen at random is a female and enjoys her role in the organisation?d. What is the probability that a respondent chosen at random is a female or enjoys her/his role in the organisation?e. What is the probability that a respondent chosen at random is a male or a female?
Solution
a. Contingency Table:
| Male | Female | Total | |
|---|---|---|---|
| Enjoy Role | 136 | 224 | 360 |
| Don't Enjoy | 104 | 36 | 140 |
| Total | 240 | 260 | 500 |
b. The probability that a respondent chosen at random enjoys his/her role in the organisation is the total number of people who enjoy their role divided by the total number of respondents. So, P(Enjoy Role) = 360/500 = 0.72 or 72%.
c. The probability that a respondent chosen at random is a female and enjoys her role in the organisation is the number of females who enjoy their role divided by the total number of respondents. So, P(Female and Enjoy Role) = 224/500 = 0.448 or 44.8%.
d. The probability that a respondent chosen at random is a female or enjoys his/her role in the organisation is the sum of the probabilities of being a female and enjoying the role minus the probability of being a female and enjoying the role (since these events can occur simultaneously). So, P(Female or Enjoy Role) = P(Female) + P(Enjoy Role) - P(Female and Enjoy Role) = 260/500 + 360/500 - 224/500 = 0.792 or 79.2%.
e. Since the respondents can only be male or female, the probability that a respondent chosen at random is a male or a female is 1 or 100%.
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