Question

If a certain middle hits the target with the probability of 30% find the number of missiles which should be fired so that prob of hitting the target is 80%?

I have these to problems for HW and having some difficulties trying to solve for them how would I go about solving the problems?

Answer 1

P(hitting target) = 0.3

P(not hitting) = 1 - 0.3 = 0.7

Consider n missiles. P(at least one of the n missiles hitting) = 1 - P(none of the n missiles hitting target)

Here, P(at least one of the n missiles hitting) = 0.8

1 - P(none of the n missiles hitting) = 0.8

1 - P(none of the n missiles hitting) = 1 - 0.7ⁿ = 0.8

0.7ⁿ = 0.2

Take log on both side

n log 0.7 = log 0.2

n = (log 0.2)/(log 0.7)

n = 4.51

= 5

5 missiles must eb fired so that probability of hitting the target is 80%