The table below shows the results of a survey that asked 2881 people whether the
ID: 3313218 • Letter: T
Question
The table below shows the results of a survey that asked 2881 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 225 459 793 1477
Female 206 450 748 1404
Total 431 909 1541 2881
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 Yes, because no females are frequently involved in charity work.
B. No, because no females are frequently involved in charity work.
C.Yes, because 206 females are frequently involved in charity work.
D.No, because206females are frequently involved in charity work.
Explanation / Answer
from above given contingency table:
a) probability that the person is frequently or occasionally involved in charity work =(431+909)/2881=0.465
b) P(being female or not being involved) =(206+450+748+793)/2881 =0.763
c)P(being male or being frequently involved) =(225+459+793+206)/2881=0.584
d) P(being female or not being frequently involved) =(206+450+748+459+793)/2881=0.922
e) D.No, because 206 females are frequently involved in charity work.
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