A rifleman is firing at a distant target and | vedclass

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(B) Let $n$ be the number of rounds fired.Probability of hitting the target in a single trial, $p = 10 \% = 0.1$.Probability of missing the target in

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(B) Let $n$ be the number of rounds fired.Probability of hitting the target in a single trial, $p = 10 \% = 0.1$.Probability of missing the target in a single trial, $q = 1 - p = 0.9$.The probability of hitting the target at least once in $n$ trials is given by $P(X \geq 1) = 1 - P(X = 0) = 1 - q^n$.We want this probability to be greater than $50 \%$, so:$1 - (0.9)^n > 0.5$$(0.9)^n Now, we test values for $n$:For $n = 6$, $(0.9)^6 = 0.531441 > 0.5$.For $n = 7$, $(0.9)^7 = 0.4782969 Thus, the least number of rounds required is $n = 7$.

$A$ rifleman is firing at a distant target and has only $10 \%$ chance of hitting it. The least number of rounds he must fire to have more than $50 \%$ chance of hitting it at least once, is

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