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Probability

Question
CBSEENMA12033858
Wired Faculty App

The probability of a man hitting a target is 1 fourth. He fires 7 times. What is the probability of his hitting at least twice the target?

Solution

Here n = 7
    straight p space equals 1 fourth comma space space straight q space equals space 1 minus straight p space equals space 1 minus 1 fourth space equals space 3 over 4
P(hitting at least twice) = 1 - [P(0) + P(1)]
                      equals space 1 minus open square brackets straight C presuperscript 7 subscript 0 space open parentheses 3 over 4 close parentheses to the power of 7 space plus space straight C presuperscript 7 subscript 1 open parentheses 1 fourth close parentheses to the power of 1 space open parentheses 3 over 4 close parentheses to the power of 6 close square brackets space equals space 1 minus open square brackets 1 space cross times space open parentheses 3 over 4 close parentheses to the power of 7 plus space 7 over 1 cross times 1 fourth cross times open parentheses 3 over 4 close parentheses to the power of 6 close square brackets space equals space 1 minus open parentheses 3 over 4 close parentheses to the power of 6 space open square brackets 3 over 4 plus 7 over 4 close square brackets space equals space 1 minus 729 over 4096 cross times 5 over 2 space equals space 1 minus 3645 over 4096 space equals space 1 minus 3645 over 8192 space equals space fraction numerator 8192 minus 3645 over denominator 8192 end fraction space equals 4547 over 8192

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