Question

Select the correct answer.

of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit
to climb the mountain. What is the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta?
OA
OC
OD.
Answer as a fraction

Answer 1

As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.

Explanation:

Let the number of fit men is x.

Now,

we know

x = 12% of 200 men

x =
`(12)/(100)` ×200

x = 0.12 × 200

= 24 men.

Given,

The 60 people are fit to climb the Mount Shasta ,24 of them are men,

so there must be

60 - 24 = 36 women who are fit to climb the mountain.

The probability of a person picked at random from the group is a male or is fit to climb Mount Shasta is the sum total of the probability of picking a fit male and the probability of picking a fit female is,

P(male or fit) = P(male and fit) + P(female and fit)

P(male or fit) = P(male) × P(fit | male) + P(female) × P(fit | female)

P(male or fit) = (
`(200)/(500)`) ×(
`(24)/(200)`) + (
`(300)/(500)`) × (
`(36)/(300)`)

=.4 × .12 + .6 × .12

= 0.048 + 0.072

=.12

So,

P(male or fit) ≈ 0.12

As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.