The probability that a person wins a prize on | vedclass

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

Question

(C) Let $n = 5$ be the number of lottery tickets purchased. Let $p$ be the probability of winning a prize on a single ticket,so $p = \frac{1}{4}$. Let

Vedclass · Accepted Answer

$\frac{781}{1024}$

Vedclass · Answer

(C) Let $n = 5$ be the number of lottery tickets purchased. Let $p$ be the probability of winning a prize on a single ticket,so $p = \frac{1}{4}$. Let $q$ be the probability of not winning a prize on a single ticket,so $q = 1 - p = 1 - \frac{1}{4} = \frac{3}{4}$. We want to find the probability of winning at least one prize,which is $P(X \ge 1)$. Using the complement rule,$P(X \ge 1) = 1 - P(X = 0)$. The probability of winning zero prizes in $5$ trials is given by the binomial distribution formula $P(X = k) = \binom{n}{k} p^k q^{n-k}$. For $k = 0$,$P(X = 0) = \binom{5}{0} (\frac{1}{4})^0 (\frac{3}{4})^5 = 1 	imes 1 	imes \frac{243}{1024} = \frac{243}{1024}$. Therefore,$P(X \ge 1) = 1 - \frac{243}{1024} = \frac{1024 - 243}{1024} = \frac{781}{1024}$.

The probability that a person wins a prize on a lottery ticket is $\frac{1}{4}$. If he purchases $5$ lottery tickets at random,then the probability that he wins at least one prize is

Similar Questions

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

The incidence of occupational disease in an industry is such that the workmen have a $10 \%$ chance of suffering from it. The probability that out of $5$ workmen,$3$ or more will contract the disease is

If a die is thrown $7$ times,what is the probability of getting exactly $5$ four times?

If the mean and variance of a binomial variate $X$ are $\frac{4}{3}$ and $\frac{8}{9}$ respectively,then $P(X=2)=$

$A$ coin is tossed $100$ times. What is the probability of getting a head an odd number of times?

Vedclass Test Series

Exam Paper Generator

Online Exam Module