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 problem is solved if at least one of them solves it.It is easier to calculate the probability that the problem is not solved by anyone.The probability that $A$ does not solve the problem is $P(A') = 1 - \frac{1}{2} = \frac{1}{2}$.The probability that $B$ does not solve the problem is $P(B') = 1 - \frac{1}{3} = \frac{2}{3}$.The probability that $C$ does not solve the problem is $P(C') = 1 - \frac{1}{4} = \frac{3}{4}$.Since these events are independent,the probability that none of them solve the problem 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 $A, B$,and $C$. 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

The probability of hitting a target by three marksmen are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that one and only one of them will hit the target when they fire simultaneously,is

$A$ draws two cards with replacement from a pack of $52$ cards and $B$ throws a pair of dice. What is the chance that $A$ gets both cards of the same suit and $B$ gets a total of $6$?

$4$ coins are tossed once. Find the probability of getting exactly $3$ tails.

For the two events $A$ and $B$,$P(A) = 0.38$ and $P(B) = 0.41$. What is the value of $P(\text{not } A)$?

An urn contains $25$ balls numbered $1$ to $25$. Suppose an odd number is considered a 'success'. $2$ balls are drawn from the urn with replacement. Find the probability of getting two successes.

Vedclass Test Series

Exam Paper Generator

Online Exam Module