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 Male Female Total 428 Frequently OccasionallyNot at all Total 795 1472 1378 1536 2850 456 430 886 221 207 741 (a) The person is frequently or occasionally involved 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.

Explanation / Answer

(a) Probability that the person is involved frequently or occasionally in charity work

= (428 + 886) / 2850

= 0.4611.

(b) Probability that the person is female and not involved in charity work at all

= (1378 + 795) / 2850

= 0.7625.

(c) The probability that the person is not frequently involved in charity work given that she is female

= (430 + 741) / 1378

= 0.8498.

(d) Since 207 people are both female and frequently involved in charity work, the events are not mutually exclusive.

=

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