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.

Answer 1

Answer:

A. P(success/age≥60) = 12.5%

B. Yes, the success is independent of age.

Step-by-step explanation:

Probability of success, given that a climber is at least 60 years old is calculated using conditional probability rule

P(A|B) = P(A n B)/P(B)

Probability of success given that a climber is at least 60 years old is given by

P(success|age≥60) = P(success n age ≥ 60)/P(age ≥ 60) = 0.005/0.04

= 0.125

P(success|age≥60) = 12.5%

B. The success is independent on age

Answer 2

Probabilities are used to determine the chances of an event.

• The probability of success, given that a climber is at least 60 years old is 0.125
• The probabilities are not independent

Let (A) represents the event that the climber succeeds, and (B) represents the event that the climber is at least 60 years old.

So, we have:

$\mathbf{P(A) = 31\%}$

$\mathbf{P(B) = 0.04}$

$\mathbf{P(A\ and\ B) = 0.005}$

(a) The probability of success, given that a climber is at least 60 years old.

This is calculated as:

$\mathbf{P(A|B) = \frac{P(A\ and\ B)}{P(B)}}$

So, we have:

$\mathbf{P(A|B) = \frac{0.005}{0.04}}$

$\mathbf{P(A|B) = 0.125}$

(b) Are the probabilities independent?

Two events A and B are independent, if:

$\mathbf{P(A\ and\ B) = P(A) \times P(B)}$

So, we have:

$\mathbf{P(A\ and\ B) = 31\% \times 0.04}$

$\mathbf{P(A\ and\ B) = 0.0124}$

From the question, we have:

$\mathbf{P(A\ and\ B) = 0.005}$

Hence, the probabilities are not independent.

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