A problem in Mathematics is given to three st | vedclass

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

Question

(A) Let $P(A), P(B),$ and $P(C)$ be the probabilities of students $A, B,$ and $C$ solving the problem respectively.$P(A) = \frac{1}{2}, P(B) = \frac{1

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(A) Let $P(A), P(B),$ and $P(C)$ be the probabilities of students $A, B,$ and $C$ solving the problem respectively.$P(A) = \frac{1}{2}, P(B) = \frac{1}{3}, P(C) = \frac{1}{4}$.The probability that the problem is not solved by $A$ is $P(A') = 1 - \frac{1}{2} = \frac{1}{2}$.The probability that the problem is not solved by $B$ is $P(B') = 1 - \frac{1}{3} = \frac{2}{3}$.The probability that the problem is not solved by $C$ is $P(C') = 1 - \frac{1}{4} = \frac{3}{4}$.The probability that the problem is not solved by any of them is $P(	ext{none}) = P(A') 	imes P(B') 	imes P(C') = \frac{1}{2} 	imes \frac{2}{3} 	imes \frac{3}{4} = \frac{6}{24} = \frac{1}{4}$.The probability that the problem is solved is $P(	ext{solved}) = 1 - P(	ext{none}) = 1 - \frac{1}{4} = \frac{3}{4}$.

$A$ problem in Mathematics is given to three students $A, B, C$ and their respective probabilities of solving the problem are $\frac{1}{2}, \frac{1}{3},$ and $\frac{1}{4}$. What is the probability that the problem is solved?

Similar Questions

If $A$ and $B$ are two events of a random experiment,$P(A) = 0.25$,$P(B) = 0.5$ and $P(A \cap B) = 0.15$,then $P(A \cap \bar{B}) = $

From a pack of $52$ cards,one card is drawn at random. The probability that it is either a king or a queen is:

Check whether the following probabilities $P(A) = 0.5$,$P(B) = 0.4$,and $P(A \cup B) = 0.8$ are consistently defined.

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$. Then,the probability that both of them occur together is:

$A$ mathematics problem is given to three students $A, B$,and $C$. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?

Vedclass Test Series

Exam Paper Generator

Online Exam Module