Question

The table below shows the results of a survey that asked 2848 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (d). Frequently Occasionally Not at all Total Male 227 792 1471 Female 202 430 745 1377 Total 429 882 1537 2848 320 452 (a) Find the probability that the person is frequently or occasionally involved in charity work P(being frequently involved or being occasionally involved) - (Round to the nearest thousandth as needed.) (b) Find the probability that the person is female or not involved in charity work at all. P(being female or not being involved) (Round to the nearest thousandth as needed.) (c) Find the probability that the person is male or frequently involved in charity work P(being male or being frequently involved) (Round to the nearest thousandth as needed.) (d) Find the probability that the person is female or not frequently involved in charity work. P(being female or not being frequently involved) (Round to the nearest thousandth as needed.)

Answer 1

	Frequently	Occasionally	Not at all	Total
Male	227	452	792	1471
Female	202	430	745	1377
Total	429	882	1537	2848

a) P(Frequently or occasionally involved) =  (429+882)/2848 = 0.460

b) P(Female or Not at all involved) = P(Female) + P(Not at all) - P(Female and Not at all)

= 1377/2848 + 1537/2848 - 745/2848 = 0.762

c) P(Male or Frequently) = P(Male) + P(Frequently) - P(Male and Frequently)

= 1471/2848 + 429/2848 - 227/2848 = 0.587

d) P(Female or not Frequently involved) = P(Female) + P(not Frequently) - P(Female and not Frequently)

= 1377/2848 + (882+1537)/2848 - (430+745)/2848

= 0.920