Question

In a group of college students, the ratio of men to women is 3:1 (i.e., 3 to 1). In a recent survey, 40% of the men in this group selected hiking as their favorite outdoor activity whereas 35% 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?

Answer 1

0.3875

Explanation:

Given that in a group of college students, the ratio of men to women is 3:1 (i.e., 3 to 1). In a recent survey, 40% of the men in this group selected hiking as their favorite outdoor activity whereas 35% of the women in the group selected hiking as their favorite outdoor activity

From the above information we find that

P(Men) = 0.75 and P(women) = 0.25 (since men:women = 3:1)

Out of men prob for not selecting hiking as their favorite outdoor activity

`=1-0.6 = 0.4`

Out of women prob for not selecting hiking as their favorite outdoor activity

`=1-0.35 = 0.65`

Prob for a randomly selected person that hiking is not his/her favorite outdoor activity = Prob (man and not selected activitiy) + P(women and not selected activity) (since men and women are mutually exclusive and exhaustive)

=
`0.75(0.4)+0.25(0.35)\\= 0.30+0.0875\\\\=0.3875`