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Probability

Question
CBSEENMA12033733

A can hit a target 4 times in 5 shots, B 3 times in 4 shots, and C 2 times in 3 shots. Calculate the probability that
(i) A B, C all may hit    (ii) B, C may hit and A may lose.

Solution
Let E1 , E2 , E3 be the events ‘A hits a shot’, ‘B hits a shot,’ ‘C hits a shot’ respectively.
therefore space space space space straight P left parenthesis straight E subscript 1 right parenthesis space equals space 4 over 5 comma space space straight P left parenthesis straight E subscript 2 right parenthesis space equals 3 over 4 comma space space straight P left parenthesis straight E subscript 3 right parenthesis space equals space 2 over 3
(i) P(A, B, C all may hit) = straight P left parenthesis straight E subscript 1 space straight E subscript 2 space straight E subscript 3 right parenthesis
                                 equals space straight P left parenthesis straight E subscript 1 right parenthesis thin space straight P left parenthesis straight E subscript 2 right parenthesis thin space straight P left parenthesis straight E subscript 3 right parenthesis space equals space 4 over 5 cross times 3 over 4 cross times 2 over 3 space equals 2 over 5
(ii) P(B, C may hit and A may lose)
                              equals space straight P left parenthesis straight E subscript 2 space straight E subscript 3 space straight E with bar on top subscript 1 right parenthesis space equals space straight P left parenthesis straight E subscript 2 right parenthesis thin space straight P left parenthesis straight E subscript 3 right parenthesis thin space straight P left parenthesis straight E with bar on top subscript 1 right parenthesis
equals space straight P left parenthesis straight E subscript 2 right parenthesis space thin space straight P left parenthesis straight E subscript 3 right parenthesis space left square bracket 1 minus straight P left parenthesis straight E subscript 1 right parenthesis right square bracket
space equals 3 over 4 cross times 2 over 3 cross times open parentheses 1 minus 4 over 5 close parentheses space equals space 3 over 4 cross times 2 over 3 cross times 1 fifth space equals 1 over 10

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