A rifleman is firing at a distant target and | vedclass

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

Question

(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

Similar Questions

The probability of getting either all heads or all tails for exactly the second time in the $3^{rd}$ trial,if in each trial three coins are tossed,is

$A$ pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is

The probability that a person who undergoes a bypass surgery will recover is $0.6$. The probability that of the $6$ patients who undergo similar operations,half of them will recover is:

Minimum number of times a fair coin must be tossed,so that the probability of getting at least one head,is more than $99 \%$ is

One hundred identical coins,each with probability $p$ of showing up heads,are tossed once. If $0 < p < 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins,then the value of $p$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module