Question

Over 1,000 people try to climb Mt. Everest every year. Of those who try to climb Everest, 31 percent succeed. The probability that a climber is at least 60 years old is 0.04. The probability that a climber is at least 60 years old and succeeds in climbing Everest is 0.005.

a. Find the probability of success, given that a climber is at least 60 years old.
b. Is success in climbing Everest independent of age?

Answer 1

A- 0.125

B- Success of climbing mount Everest is independent of age.

Explanation:

A.

Let x denote success in climbing Mount Everest

Let y denote the climber is at least 60 years old.

Therefore,

P(x) = 0.31

P(y) = 0.04

P( x ∩ y) = 0.005

Probability of success when the climber is at least 60 years old =

P( x ∩ y) ÷ P(y) = 0.005 ÷ 0.04 = 0.125.

B.

The success rate is independent of age as there are both success and failure rates across board on the scale of ages of climbers.