The probabilities of A, B, and C solving a pr | vedclass

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

Question

(B) Let $P(A) = \frac{1}{3}, P(B) = \frac{2}{7}, P(C) = \frac{3}{8}$.Then the probabilities of not solving the problem are $P(A') = 1 - \frac{1}{3} =

Vedclass · Accepted Answer

$\frac{25}{56}$

Vedclass · Answer

(B) Let $P(A) = \frac{1}{3}, P(B) = \frac{2}{7}, P(C) = \frac{3}{8}$.Then the probabilities of not solving the problem are $P(A') = 1 - \frac{1}{3} = \frac{2}{3}, P(B') = 1 - \frac{2}{7} = \frac{5}{7},$ and $P(C') = 1 - \frac{3}{8} = \frac{5}{8}$.Exactly one of them solves the problem if ($A$ solves and $B, C$ do not) $OR$ ($B$ solves and $A, C$ do not) $OR$ ($C$ solves and $A, B$ do not).Required probability $= P(A)P(B')P(C') + P(A')P(B)P(C') + P(A')P(B')P(C)$$= (\frac{1}{3} 	imes \frac{5}{7} 	imes \frac{5}{8}) + (\frac{2}{3} 	imes \frac{2}{7} 	imes \frac{5}{8}) + (\frac{2}{3} 	imes \frac{5}{7} 	imes \frac{3}{8})$$= \frac{25}{168} + \frac{20}{168} + \frac{30}{168} = \frac{75}{168} = \frac{25}{56}$.

The probabilities of $A, B,$ and $C$ solving a problem are $\frac{1}{3}, \frac{2}{7},$ and $\frac{3}{8}$ respectively. If all three try to solve the problem simultaneously,the probability that exactly one of them will solve it is:

Similar Questions

If two dice are thrown simultaneously,then the probability that $1$ comes on the first die is

The probability of a student qualifying for $IITJEE$ and $EAMCET$ are $\frac{1}{5}$ and $\frac{3}{5}$ respectively. The probability that the student qualifies for at least one of these tests is:

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the events $B$ and $C$.

If $A$ and $B$ are events of a sample space such that $P(A \cup B) = \frac{3}{4}$, $P(A \cap B) = \frac{1}{4}$, and $P(\bar{A}) = \frac{2}{3}$, then $P(\bar{A} \cap B)$ is

The probability that Ajay will not appear in the $JEE$ exam is $p = \frac{2}{7}$,while the probability that both Ajay and Vijay will appear in the exam is $q = \frac{1}{5}$. Then the probability that Ajay will appear in the exam and Vijay will not appear is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module