If A and B are events such that P(A cup B) = | vedclass

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

Question

(A) Given: $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(\overline{A}) = \frac{2}{3}$.Since $P(A) = 1 - P(\overline{A})$,we have $P(A

Vedclass · Accepted Answer

$5/12$

Vedclass · Answer

(A) Given: $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(\overline{A}) = \frac{2}{3}$.Since $P(A) = 1 - P(\overline{A})$,we have $P(A) = 1 - \frac{2}{3} = \frac{1}{3}$.Using the addition theorem: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the values: $\frac{3}{4} = \frac{1}{3} + P(B) - \frac{1}{4}$.$P(B) = \frac{3}{4} + \frac{1}{4} - \frac{1}{3} = 1 - \frac{1}{3} = \frac{2}{3}$.We need to find $P(\overline{A} \cap B)$.Note that $P(\overline{A} \cap B) = P(B) - P(A \cap B)$.$P(\overline{A} \cap B) = \frac{2}{3} - \frac{1}{4} = \frac{8 - 3}{12} = \frac{5}{12}$.

If $A$ and $B$ are events such that $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(\overline{A}) = \frac{2}{3}$,then what is the value of $P(\overline{A} \cap B)$?

Similar Questions

What is the probability of getting a doublet when two dice are thrown?

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

Let $A$ and $B$ be two events in a random experiment. If $P(A \cap \overline{B}) = 0.1$,$P(\overline{A} \cap B) = 0.2$ and $P(B) = 0.5$,then $P(\overline{A} \cap \overline{B}) = $

If one ticket is selected at random from $30$ tickets,each with a distinct number from $1$ to $30$,then the probability that the number on the selected ticket is a multiple of $3$ or $5$ is

In a competition,$A, B$,and $C$ are participating. The probability that $A$ wins is twice that of $B$,and the probability that $B$ wins is twice that of $C$. Then,the probability that $A$ loses is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module