For three events A, B and C,P(text{Exactly on | vedclass

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

Question

(C) Let $P(A), P(B), P(C)$ be the probabilities of events $A, B, C$. Given: $P(A) + P(B) - 2P(A \cap B) = \frac{1}{4}$ ... $(1)$ $P(B) + P(C) - 2P(B \

Vedclass · Accepted Answer

$\frac{7}{16}$

Vedclass · Answer

(C) Let $P(A), P(B), P(C)$ be the probabilities of events $A, B, C$. Given: $P(A) + P(B) - 2P(A \cap B) = \frac{1}{4}$ ... $(1)$ $P(B) + P(C) - 2P(B \cap C) = \frac{1}{4}$ ... $(2)$ $P(C) + P(A) - 2P(C \cap A) = \frac{1}{4}$ ... $(3)$ Adding $(1), (2),$ and $(3)$,we get: $2[P(A) + P(B) + P(C)] - 2[P(A \cap B) + P(B \cap C) + P(C \cap A)] = \frac{3}{4}$ Dividing by $2$: $[P(A) + P(B) + P(C)] - [P(A \cap B) + P(B \cap C) + P(C \cap A)] = \frac{3}{8}$ We know that $P(A \cup B \cup C) = [P(A) + P(B) + P(C)] - [P(A \cap B) + P(B \cap C) + P(C \cap A)] + P(A \cap B \cap C)$. Substituting the values: $P(A \cup B \cup C) = \frac{3}{8} + \frac{1}{16} = \frac{6+1}{16} = \frac{7}{16}$.

Similar Questions

Let $p$ denote the probability that a man aged $x$ years will die in a year. The probability that out of $n$ men $A_1, A_2, A_3, ..., A_n$ each aged $x$,$A_1$ will die in a year and will be the first to die,is

Let $A$ be the set of all $4$-digit natural numbers whose exactly one digit is $7$. Then the probability that a randomly chosen element of $A$ leaves a remainder of $2$ when divided by $5$ is ..... .

If $A$ and $B$ are two independent events such that $P(B)=\frac{2}{7}$ and $P\left(A \cup B^c\right)=0.8$, then $P(A \cup B)$ $=$

$A$ fair die is rolled indefinitely. Player $A$ wins if two consecutive rolls show $3$ or $5$, and player $B$ wins if two consecutive rolls show $1$ or $2$ or $4$ or $6$. The probability that player $A$ wins is:

Let $X$ and $Y$ be two events such that $P(X \cup Y) = P(X \cap Y)$.
Statement $1$: $P(X \cap Y') = P(X' \cap Y) = 0$.
Statement $2$: $P(X) + P(Y) = 2P(X \cap Y)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module