Let A and B be two events such that the proba | vedclass

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

Question

(A) Given that,the probability that exactly one of them occurs is $P(A \cup B) - P(A \cap B) = \frac{2}{5} \dots (i)$ The probability that $A$ or $B$

Vedclass · Accepted Answer

$0.1$

Vedclass · Answer

(A) Given that,the probability that exactly one of them occurs is $P(A \cup B) - P(A \cap B) = \frac{2}{5} \dots (i)$ The probability that $A$ or $B$ occurs is $P(A \cup B) = \frac{1}{2} \dots (ii)$ We know that the probability of exactly one event occurring is given by $P(A \cup B) - P(A \cap B)$. Substituting the values from $(i)$ and $(ii)$: $\frac{1}{2} - P(A \cap B) = \frac{2}{5}$ $P(A \cap B) = \frac{1}{2} - \frac{2}{5}$ $P(A \cap B) = \frac{5 - 4}{10} = \frac{1}{10} = 0.1$

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$,then the probability of both of them occurring together is

Similar Questions

In a lottery containing $35$ tickets,exactly $10$ tickets bear a prize. If a ticket is drawn at random,then the probability of not getting a prize is

Three coins are tossed. Describe three events which are mutually exclusive but not exhaustive.

Let $A$ and $B$ be two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$ and $P(\bar{A}) = \frac{1}{4}$,where $\bar{A}$ stands for the complement of the event $A$. Then the events $A$ and $B$ are

If three students $A, B, C$ independently solve a problem with probabilities $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively,then the probability that the problem will be solved is

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module