The probability that a man hits a target when he fires is If he fires 10 rounds, what is the probability of his hitting the target at least twice? - Wired Faculty

Probability

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The probability that a man hits a target when he fires is $1 fifth.$ If he fires 10 rounds, what is the probability of his hitting the target at least twice?

Solution

Here n = 10, $straight p space equals space 1 fifth comma space space space space space space straight q space equals space 1 minus 1 fifth space equals space 4 over 5$
P(hitting at least twice) = 1 - [P(0) + P(1)]
$equals space 1 minus space open square brackets straight C presuperscript 10 subscript 0 space open parentheses 4 over 5 close parentheses to the power of 10 space plus space straight C presuperscript 10 subscript 1 space open parentheses 4 over 5 close parentheses to the power of 9 space open parentheses 1 fifth close parentheses close square brackets space equals space 1 minus space open parentheses 4 over 5 close parentheses to the power of 9 space open square brackets 1 space cross times space 4 over 5 plus 10 over 5 close square brackets space equals space 1 minus open parentheses 4 over 5 close parentheses to the power of 9 space open parentheses 14 over 5 close parentheses space equals space 1 minus 0.3758 space equals space 0.6242$

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Probability

The probability that a man hits a target when he fires is $1 fifth.$ If he fires 10 rounds, what is the probability of his hitting the target at least twice?

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