The probability of a man hitting a target is (1/10) The least number of shots required, so that the probability of his hitting the target at least once is greater than (1/4), is .

Question

The probability of a man hitting a target is (1/10) The least number of shots required, so that the probability of his hitting the target at least once is greater than (1/4), is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We have, 1 - (probability of all shots result in failure )>(1/4) ⇒ 1-((9/10)) n >(1/4) ⇒ (3/4)>((9/10))n ⇒ n ≥ 3

Q. The probability of a man hitting a target is $\frac{1}{10}$ The least number of shots required, so that the probability of his hitting the target at least once is greater than $\frac{1}{4},$ is _______.

We have, 1 - (probability of all shots result in failure $) > \frac{1}{4}$
$\Rightarrow 1 - (\frac{9}{10})^{n} > \frac{1}{4}$
$\Rightarrow \frac{3}{4} > (\frac{9}{10})^{n}$
$\Rightarrow n \geq 3$

Q. The probability of a man hitting a target is 101​ The least number of shots required, so that the probability of his hitting the target at least once is greater than 41​, is _______.

We have, 1 - (probability of all shots result in failure )>41​ ⇒1−(109​)n>41​ ⇒43​>(109​)n ⇒n≥3

Q. The probability of a man hitting a target is $\frac{1}{10}$ The least number of shots required, so that the probability of his hitting the target at least once is greater than $\frac{1}{4},$ is _______.

We have, 1 - (probability of all shots result in failure $) > \frac{1}{4}$
$\Rightarrow 1 - (\frac{9}{10})^{n} > \frac{1}{4}$
$\Rightarrow \frac{3}{4} > (\frac{9}{10})^{n}$
$\Rightarrow n \geq 3$