The table shows the results of a survey that asked 2850 people whether they are

Question

The table shows the results of a survey that asked 2850 people whether they are involved in any type of charity work. A person is selected at random from the sample. Find the probability of each event.

a) The person is frequently or occasionally involed in charity work.

b) The person is female or not involved in charity work at all.

c) The person is not frequently involved in charity work, given that she is female.

d) Are the events "being female" and "being frequently involved in charity work" mutually exclusive? Explain.

Frequently Occasionally Not at all Total Male 221 456 795 1472 Female 207 430 741 1378 Total 428 886 1536 2850

Explanation / Answer

a) P(the person is frequently or occasionally involed in charity work) = (428+886)/2850 = 0.461

b) P(the person is female or not involved in charity work at all) = (1378+795)/2850 = 0.762

c) P(the person is not frequently involved in charity work | female) = (430+741)/1378 = 0.8498

d) No, the events "being female" and "being frequently involved in charity work" are not mutually exclusive, because there are female who are frequently involved in charity work. Two events are mutually nexclusive only if there is nothing in common in those two events.

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