A rifle man firing at a distant target and has only 10% chance of hitting it. The minimum number of rounds he must fire in order to have 50% chance of hitting it atleast once is
A
6
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B
7
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C
8
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D
9
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Solution
The correct option is B 7 The probability of hitting in one shot =10100=110 If he fires n shots, the probability of hitting atleast one =1−(1−110)n=1−(910)n=50%=50100=12⇒(910)n=(12) ∴n{log9−log10}=log1−log2⇒n{2log3−1}=0−log2∴n=log21−2log3=0.30103001−2×0.4771213=6.6 Hence, n =7