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 - 0.7^{n} =
0.8

0.7^{n} = 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%**

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