n a group of college students, the ratio of men to women is 3:2 (i.e., 3 to 2).

Question

n a group of college students, the ratio of men to women is 3:2 (i.e., 3 to 2). In a recent survey, 65% of the men in this group selected hiking as their favorite outdoor activity whereas 40% of the women in the group selected hiking as their favorite outdoor activity. An individual is randomly selected from this group. What is the probability that hiking is not his/her favorite outdoor activity? Round your result to 2 significant places after the decimal (For example, 0.86732 should be entered as 0.87).

Explanation / Answer

Given,

P(Men) = 3/(3 + 2) = 3/5

P(Women) = 2/(3 + 2) = 2/5

P(Hikin |Men) = 0.65

P(Hiking| Women) = 0.40

So,

P(Hiking is not his/her favorite outdoor activity)

= P(Men)*P(Not hiking | Men) + P(Women)*P(Not hiking | Women)

= (3/5)*(1 - 0.65) + (2/5)*(1 - 0.40)

= 0.45

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