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The probability of a missile hitting the target successfully in a trial is 0.2. Five successful hitting are needed to destroy a particular target. What is the probability that the target will be destroyed in the 7th trial?

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Does this mean exactly that the 7th missile destroys it, or that it could already be destroyed by missile 5 or 6? – Euler....IS_ALIVE Sep 9 '12 at 6:47
My comment on your other question fully applies. – Did Sep 9 '12 at 7:51

So you want the probability of exactly $4$ "successes" in the first $6$ trials, and then a success on the $7$th trial. The probability is $$\binom{6}{4}(0.2)^4(0.8)^2(0.2).$$

The part before the final $0.2$ is a straight Binomial Distribution calculation.

I prefer problems about picking jelly beans from a large jar.

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