The table below shows the results of a survey that asked 28832883 people whether
ID: 3309426 • Letter: T
Question
The table below shows the results of a survey that asked 28832883 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
228
452
795
1475
Female
209
450
749
1408
Total
437
902
1544
2883
a) Find the probability that the person is frequently or occasionally involved in charity work.
Upper 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? Choose answer below.
A. No, because 209 females are frequently involved in charity work.
B. No, because no females are frequently involved in charity work.
C. Yes, because 209 females are frequently involved in charity work.
D. Yes, because no females are frequently involved in charity work.
Frequently
Occasionally
Not at all
Total
Male
228
452
795
1475
Female
209
450
749
1408
Total
437
902
1544
2883
Explanation / Answer
A) P(frequently or occasionally) = P(frequently) + P(occasionally)
= 437/2883 + 902/2883
= 0.464
B) P(female or not being involved) = P(female) + P(not being involved) - P(female and not being involved)
= 1408/2883 + 1544/2883 - 749/2883
= 0.764
C) P(male or frequently) + P(male) + P(frequently) - P(male and frequently)
= 1475/2883 + 437/2883 - 228/2883
= 0.584
D) P(female or not frequently) = P(female) + P(not frequently) - P(female and not frequently)
= 1408/2883 + (902 + 1544)/2883 - (450 + 749)/2883
= 0.917
E) Option-A)
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