The probabilities of solving a specific probl | vedclass

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

Question

(B) Let $P(A) = \frac{1}{2}$ be the probability that $A$ solves the problem.Let $P(B) = \frac{1}{3}$ be the probability that $B$ solves the problem.Th

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(B) Let $P(A) = \frac{1}{2}$ be the probability that $A$ solves the problem.Let $P(B) = \frac{1}{3}$ be the probability that $B$ solves the problem.Then,$P(A') = 1 - P(A) = 1 - \frac{1}{2} = \frac{1}{2}$ and $P(B') = 1 - P(B) = 1 - \frac{1}{3} = \frac{2}{3}$.The probability that exactly one of them solves the problem is given by $P(A \cap B') + P(B \cap A')$.Since the events are independent,this is equal to $P(A) \cdot P(B') + P(B) \cdot P(A')$.$= (\frac{1}{2} 	imes \frac{2}{3}) + (\frac{1}{3} 	imes \frac{1}{2})$$= \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$.

The probabilities of solving a specific problem independently by $A$ and $B$ are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently,find the probability that exactly one of them solves the problem.

Similar Questions

Let $N$ denote the sum of the numbers obtained when two dice are rolled. If the probability that $2^{N} < N!$ is $\frac{m}{n}$,where $m$ and $n$ are coprime,then $4m - 3n$ is equal to $......$.

If $x$ is chosen at random from the set $\{1, 2, 3, 4\}$ and $y$ is chosen at random from the set $\{5, 6, 7\}$,then the probability that $xy$ will be even is

What is the probability that a randomly selected leap year has $53$ Sundays or $53$ Mondays (in $/7$)?

$A$ card is drawn at random from a pack of $52$ cards. What is the probability that the drawn card is neither a heart nor a king?

$A$ coin is tossed three times. Let $A$ be the event of "getting three heads" and $B$ be the event of "getting a head on the first toss". Then $A$ and $B$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module