The probability of a shooter hitting a target | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the shooter fire $n$ times. These $n$ fires are $n$ Bernoulli trials. In each trial,the probability of hitting the target is $p = \frac{3}{4}$

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) Let the shooter fire $n$ times. These $n$ fires are $n$ Bernoulli trials. In each trial,the probability of hitting the target is $p = \frac{3}{4}$ and the probability of not hitting the target is $q = 1 - p = \frac{1}{4}$. The probability of hitting the target at least once is given by $P(X \geq 1) = 1 - P(X = 0)$. Here,$P(X = 0)$ is the probability of not hitting the target in any of the $n$ trials,which is $q^n = (\frac{1}{4})^n$. We are given that $P(X \geq 1) > 0.99$. Therefore,$1 - (\frac{1}{4})^n > 0.99$. This simplifies to $1 - 0.99 > (\frac{1}{4})^n$,which means $0.01 > (\frac{1}{4})^n$. This is equivalent to $\frac{1}{100} > \frac{1}{4^n}$,or $4^n > 100$. Testing values for $n$: For $n = 3$,$4^3 = 64 For $n = 4$,$4^4 = 256 > 100$. Thus,the minimum number of times the shooter must fire is $4$.

The probability of a shooter hitting a target is $\frac{3}{4}$. What is the minimum number of times he/she must fire so that the probability of hitting the target at least once is greater than $0.99$?

Similar Questions

Two cards are drawn at random one after the other with replacement from a pack of $52$ playing cards. Then the variance of the random variable of the number of spade cards among the drawn cards is

$A$ fair coin is tossed $15$ times. The probability that the tail will appear at least thrice is

$A$ student is given $6$ questions in an examination with true or false type of answers. If he writes $4$ or more correct answers, he passes in the examination. The probability that he passes in the examination is

At least how many times must a fair coin be tossed so that the probability of getting at least one head is at least $0.8$?

If $X$ has a binomial distribution with parameters $n=6, p$ and $P(X=2)=12, P(X=3)=5$,then $p=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module