Question

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?

Answer 1

1. Count how many men are fit to climb:

200 men - 100%

x men - 12 %

Then

`(200)/(x)=(100)/(12) ,\\ \\ x=(200\cdot 12)/(100)=24.`

2. 60 are fit enough to climb Mount Shasta in California, among them 24 are men, then 60-24=36 are women.

3. The probability that a person picked at random from the group is a male is
`Pr(\text{male})=(200)/(500)=0.4.`

4. The probability that a person picked at random from the group is fit to climb Mount Shasta is

`Pr(\text{fit to climb})=(60)/(500)=0.12.`

5. Use formula

`Pr(\text{male or fit to climb})=Pr(\text{male})+Pr(\text{fit to climb})-Pr(\text{male and fit to climb}).`

6.

`Pr(\text{male and fit to climb})=(24)/(500)=0.048.`

Then

7.

`Pr(\text{male or fit to climb})=0.4+0.12-0.048,`

`Pr( \text{ male or fit to climb })=0.472.`

Answer: 0.472 (or in percent near 47.2%).