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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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    My comment [on your other question](http://math.stackexchange.com/q/193073/6179) fully applies.2012-09-09

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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.