1. Count how many men are fit to climb:
200 men - 100%
x men - 12 %
Then
\(\dfrac{200}{x}=\dfrac{100}{12} ,\\ \\ x=\dfrac{200\cdot 12}{100}=24.\)
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 \(Pr(\text{male})=\dfrac{200}{500}=0.4.\)
4. The probability that a person picked at random from the group is fit to climb Mount Shasta is
\(Pr(\text{fit to climb})=\dfrac{60}{500}=0.12.\)
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.
\(Pr(\text{male and fit to climb})=\dfrac{24}{500}=0.048.\)
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%).
