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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1$\begingroup$ Does this mean exactly that the 7th missile destroys it, or that it could already be destroyed by missile 5 or 6? $\endgroup$– Euler....IS_ALIVESep 9, 2012 at 6:47
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$\begingroup$ My comment on your other question fully applies. $\endgroup$– DidSep 9, 2012 at 7:51
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1 Answer
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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.
answered Sep 9, 2012 at 6:57