A rifleman is firing at a distant target and has only 10% chance of hiting it. the least number of round he must fire in order to have more than 50% chance of hitting it at least once is:
A
11
B
9
C
7
D
5
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C
7
Given $\text{p}=\frac{1}{10}\Rightarrow\text{q}=\frac{9}{10}$
Let n be the number of rounds.
$\text{P(X}\geq1)=1-\text{P(X}=0)$
$\Rightarrow\text{P(X}\geq1)\geq0.5$
$\Rightarrow1-\text{P(X}=0)\geq0.5$
$\Rightarrow\text{P(X}=0)\leq0.5$
$\Rightarrow0.9^{\text{n}}\leq0.5$
Using log table,
$\text{n}\leq6.572\approx7$
He must fire in order to have more than
50% chance of hitting the target at least once.
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