Question

Find the probability that the person is frequently or occasionally involved in charity work.

Answer 1

Given the table below which shows the result of a survey that asked 2,881 people whether they are involved in any type of charity work.

$\begin{tabular} {|c|c|c|c|c|c|} &Frequently&Occassionally&Not at all&Total\\[1ex] Male&227&454&798&1,479\\ Female &205&450&747&1,402\\ Total&432&904&1,545&2,881 \end{tabular}$

Part A:

If a person is chosen at random, the probability that the person is frequently or occassinally involved in charity work is given by

$P(being \ frequently \ involved \ or \ being \ occassionally \ involved)\\ \\= \frac{432}{2881} + \frac{904}{2881} = \frac{1336}{2881}=\bold{0.464}$



Part B:

If a person is chosen at random, the probability that the person is female or not involved in charity work at all is given by

$P(being \ female \ or \ not \ being \ involved)\\ \\= \frac{1402}{2881} + \frac{1545}{2881}-\frac{747}{2881} = \frac{2200}{2881}=\bold{0.764}$



Part C:

If a person is chosen at random, the probability that the person is male or frequently involved in charity work is given by

$P(being \ male \ or \ being \ frequently \ involved)\\ \\= \frac{1479}{2881} + \frac{432}{2881}-\frac{227}{2881} = \frac{1684}{2881}=\bold{0.585}$



Part D:

If a person is chosen at random, the probability that the person is female or not frequently involved in charity work is given by

$P(being \ female \ or \ not \ being \ frequently \ involved)\\ \\= \frac{1402}{2881} + \frac{904}{2881} + \frac{1545}{2881}-\frac{450}{2881}-\frac{747}{2881} = \frac{2654}{2881}=\bold{0.921}$



Part E:

The events "being female" and "being frequently involved in charity work" are not mutually exclusive because being a female does not prevent a person from being frequently involved in charity work.

Indeed from the table, there are 205 females who are frequently involved in charity work.

Therefore, the answer to the question is "No, because 205 females are frequently involved charity work".