A recent survey asked 100 people (59 men and 41 women) if they thought women in
ID: 2925509 • Letter: A
Question
A recent survey asked 100 people (59 men and 41 women) if they thought women in the armed forces should be permitted to participate in combat. Thirty-seven of the men answered “yes” while 24 of the women answered “yes.” (a). What is the probability the participant chosen at random is a woman who answered “yes”? (i.e. is a woman and answered yes.)
(b). What portion of those who answered “yes” are women? (c). Is a woman more likely to answer “yes” to the question than a man is? Justify your answer. (d). Are the events “The participant is a woman” and “The participant answered ‘yes’” independent? Justify your answer with probability. (e). Are the events “The participant is a woman” and “The participant answered ‘yes’” mutually exclusive? Justify your answer.
Explanation / Answer
a) P(Woman and answered yes) = 24/100 = 0.24
b) P(Women | Yes) = 24/(24 + 37) = 24/61 = 0.3934 [Rounded off to 4 decimal places]
c) Proportion of women said "yes" = 24/41 = 0.585
Proportion of men said "yes" = 37/59 = 0.627
So,
No, women are actually less likely to answer "yes" as compared to men.
d) No,
Since P(Women | Yes) is not equal to P(Women), these two events are not independent.
e) No,
Since there are 24 women said "yes", these two events aren't mutually exclusive.