Probability Question?

Question

The probabilty of a given U.S B-17 crewman being show down on any given bombing run over germany in world war 2 is 4.5%
A- What would the probability of crewman surviving 25 bombing runs, the stipulated tour of duty?
B-What tour of duty would have given a survival rate closest to 50%?
C- What would be the life expectany of crewman, in average number of bombing runs?

Answer 1

Do you assume that being shot down on one raid is independent of being shot down on another? Because I would think that skill and experience would come into it as well...

However, if you assume the events are independent then you can multiply the probabilities together, so use
P(gets shot down on one mission) = 0.045
P(does not get shot down) = 0.955

P(doesn't get shot down on 2 missions) = 0.955 * 0.955
P(doesn't get shot down on 3 missions) = 0.955 * 0.955 * 0.955

etc etc
So A)
P(doesn't get shot down on 25 missions) = 0.955 ^25
-- you work it out on calculator, I left mine at work for the Chirstmas holidays!!!

b) Need to solve the equation
0.955 ^ n = 0.5
so take log of bth sides
log (0.955^n) = log (0.5)
use laws of logs
n log (0.995) = log (0.5)
isolate n
n = log (0.5) / log (0.995)
---again you will have to do this on your calc.

If you haven't yet studied logs, you can solve this equation using trial and improvement.

C)
No idea I'm afraid.

This question is a bit morbid. Is your teacher some sort of war freak?! I'd much rather set questions about people passing driving tests or something cheerful rather than death!!!

Answer 2

A. 31%
B. 15
C. (1-.045)^n where n is number of bombing runs


Doug