The probabilities of solving a specific probl | vedclass

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

Question

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

Vedclass · Accepted Answer

$\frac{2}{3}$

Vedclass · Answer

(C) Let $P(A)$ be the probability that $A$ solves the problem,$P(A) = \frac{1}{2}$.Let $P(B)$ be the probability that $B$ solves the problem,$P(B) = \frac{1}{3}$.The problem is solved if at least one of them solves it.The probability that the problem is not solved by either is $P(A') 	imes P(B')$.$P(A') = 1 - P(A) = 1 - \frac{1}{2} = \frac{1}{2}$.$P(B') = 1 - P(B) = 1 - \frac{1}{3} = \frac{2}{3}$.Probability that the problem is not solved $= P(A') 	imes P(B') = \frac{1}{2} 	imes \frac{2}{3} = \frac{1}{3}$.Probability that the problem is solved $= 1 - P(	ext{not solved}) = 1 - \frac{1}{3} = \frac{2}{3}$.

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 the problem is solved.

Similar Questions

When a pair of dice is thrown,what is the probability of getting an even number on each die?

If $A$ and $B$ are two events with $P(A \cup B) = 0.65$ and $P(A \cap B) = 0.15$,then find the value of $P(A^C) + P(B^C)$.

When a pair of six-faced fair dice are thrown, the probability that the sum of the numbers on the two dice is greater than $7$ is:

From the word $POSSESSIVE$,a letter is chosen at random. The probability of it being $S$ is

An experiment consists of tossing a coin and then throwing it a second time if a head occurs. If a tail occurs on the first toss,then a die is rolled once. Find the sample space.

Vedclass Test Series

Exam Paper Generator

Online Exam Module