A recent survey asked 100 people (59 men and 41 women) if they thought women in

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.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.