The probability of a jet fighter surviving a combat mission

The probability of a jet fighter surviving a combat mission is 0.8 and three fighters are needed for the success of the mission. How many fighters must be sent on the mission in order to achieve a 95% probability of success?

Solution

You need to find the minimum n so that the probability of 0-2 successes is less than or equal to 1-95% = .05.

p = .8. Thus,

Thus, find the minimum n such that C(n,0) .2^n(.8)^0 + C(n,1) .2^(n-1).8^1 + C(n,2).2^(n-2).8^2 <= .05

Rewriting

.2^n + n .2^(n-1).8 + n(n-1)/2.2^(n-2).64 <= .05

Clearly, we need for n to be >= 3, so let\'s start our table here.

As a check, for n = 3, the probability of 3 successes is .8^3 = .512, so the probability of non-success is 1 - .512 = .488, which we see in our table below.

We need to have n = 6 for the probability of non-success to be less than .05