The table below shows the results of a survey that asked 285

The table below shows the results of a survey that asked 2853 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 (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.) (e) Are the events being female and being frequently involved in charity work mutually exclusive? Explain. A. No, because 205 females are frequently involved in charity work. B. No, because no females are frequently involved in charity work. C. Yes, because no females are frequently involved in charity work. D. Yes, because 205 females are frequently involved in charity work.

Solution

(a) 436/2872 + 897/2872 = 0.464

(b) 1396/2872 +1539/2872 - 747/2872 =0.762

(c) 1476/2872+436/2872 - 227/2872 =0.587

(d) 1396/2872 + (897+1539)/2872 - (440+747)/2872 =0.921