The table below shows the results of a survey that asked 28562856 people whether they are involved in any type of charity work. a person is selected at random from the sample. complete parts (a) through (e). frequently occasionally not at all total male 225225 455455 799799 14791479 female 203203 430430 744744 13771377 total 428428 885885 15431543 28562856
Accepted Solution
A:
Given the table below which shows the result of a survey that asked
2,856 people whether they are involved in any type of charity work.
[tex]\begin{tabular}{|c|c|c|c|c|c|} &Frequently&Occassionally&Not at all&Total\\[1ex]Male&225&455&799&1,479\\Female &203&430&744&1,377\\Total&428&885&1,543&2,856\end{tabular}[/tex]
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:
[tex]P(being \ frequently \ involved \ or \ being \ occassionally \ involved)\\ \\= \frac{428}{2856} + \frac{885}{2856} = \frac{1313}{2856}=\bold{0.460}[/tex]
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:
[tex]P(being \ a \ female \ or \ not \ being \ involved)\\ \\= \frac{1377}{2856} + \frac{1543}{2856}-\frac{744}{2856} = \frac{2176}{2856}=\bold{0.762}[/tex]
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:
[tex]P(being \ a \ male \ or \ being \ frequently \ involved)\\ \\= \frac{1479}{2856} + \frac{428}{2856}-\frac{225}{2856} = \frac{1682}{2856}=\bold{0.589}[/tex]
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:
[tex]P(being \ a \ female \ or \ not \ being \ frequently \ involved)\\ \\= \frac{1377}{2856} + \frac{885}{2856} + \frac{1543}{2856}-\frac{430}{2856}-\frac{744}{2856} = \frac{2631}{2856}=\bold{0.921}[/tex]
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".