Question 1186369: A bush pilot faces the following situation. His single-engine aircraft is on fire. He could attempt to
crash land on the beach ahead, in which case he will need assistance or he could attempt to reach
an emergency strip at which he can land safely and assistance will be available. Using the estimates
given below what should he do if his objective is to stay alive?
(a) odds on reaching emergency strip versus mid-air explosion 1:4;
(b) probability of surviving mid-air explosion 0;
(c) probability of reaching beach 0.8;
(d) probability of surviving beach landing 0.5;
(e) probability of receiving necessary assistance after a beach landing
by air rescue 0.3,
by passing boat 0.2
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to break down the pilot's decision-making process:
**1. Probability of Reaching the Emergency Strip:**
* The odds of reaching the strip vs. mid-air explosion are 1:4. This means the probability of reaching the strip is 1/(1+4) = 1/5 = 0.2.
**2. Probability of Surviving the Emergency Strip Landing:**
* If he reaches the strip, he lands safely, and assistance is available. So, the probability of survival is 1.
**3. Probability of Surviving the Beach Landing:**
* Probability of reaching the beach: 0.8
* Probability of surviving the beach landing *given* he reaches the beach: 0.5
* Probability of surviving the beach landing *and* reaching the beach: 0.8 * 0.5 = 0.4
**4. Probability of Receiving Assistance After a Beach Landing:**
* Probability of assistance by air rescue: 0.3
* Probability of assistance by passing boat: 0.2
* Probability of *at least* one of these assisting: 0.3 + 0.2 - (0.3 * 0.2) = 0.5 - 0.06 = 0.44
**5. Overall Probability of Survival (Beach Landing):**
* Probability of surviving beach landing *and* getting assistance: 0.4 * 0.44 = 0.176
**6. Overall Probability of Survival (Emergency Strip):**
* Probability of reaching the strip: 0.2
* Probability of surviving the landing: 1
* Overall survival probability: 0.2 * 1 = 0.2
**7. Decision:**
The pilot has a higher chance of survival (0.2 or 20%) if he attempts to reach the emergency strip compared to attempting a beach landing (0.176 or 17.6%).
**Therefore, the pilot should attempt to reach the emergency strip.**
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