A rifleman is firing at a distance target and has only $10 %$ chance of hitting it. Then the number of rounds, he must fire in order to have more than $50 %$ chance of hitting it at least once is:

6

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Solution

The correct option is B $7$
We have,
$p = \frac{10}{100} = \frac{1}{10}$
$∴ q = \frac{9}{10}$
By the given condition,
$1 - q^{n} > \frac{1}{2}$
$\Rightarrow q^{n} < \frac{1}{2}$
$\Rightarrow {(\frac{9}{10})}^{n} < \frac{1}{2}$
Which is possible if $n$ is at least $7$
$∴ n = 7$

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A rifleman is firing at a distance target and has only 10% chance of hitting it. Then the number of rounds, he must fire in order to have more than 50% chance of hitting it at least once is:

The correct option is B 7We have, p=10100=110 ∴q=910 By the given condition, 1−qn>12 ⇒qn<12 ⇒(910)n<12 Which is possible if n is at least 7 ∴n=7

A rifleman is firing at a distance target and has only $10 %$ chance of hitting it. Then the number of rounds, he must fire in order to have more than $50 %$ chance of hitting it at least once is:

The correct option is B $7$
We have,
$p = \frac{10}{100} = \frac{1}{10}$
$∴ q = \frac{9}{10}$
By the given condition,
$1 - q^{n} > \frac{1}{2}$
$\Rightarrow q^{n} < \frac{1}{2}$
$\Rightarrow {(\frac{9}{10})}^{n} < \frac{1}{2}$
Which is possible if $n$ is at least $7$
$∴ n = 7$