A and B are independent events with P(A)=frac | vedclass

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

Question

(D) Given that $A$ and $B$ are independent events,we have $P(A \cap B) = P(A) \cdot P(B)$.From the given equation: $P(A \cup B) = 2P(B) - P(A)$.Using

Vedclass · Accepted Answer

$\frac{2}{5}$

Vedclass · Answer

(D) Given that $A$ and $B$ are independent events,we have $P(A \cap B) = P(A) \cdot P(B)$.From the given equation: $P(A \cup B) = 2P(B) - P(A)$.Using the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$,we get:$P(A) + P(B) - P(A \cap B) = 2P(B) - P(A)$.Substituting $P(A \cap B) = P(A) \cdot P(B)$:$P(A) + P(B) - P(A) \cdot P(B) = 2P(B) - P(A)$.Rearranging the terms to solve for $P(B)$:$2P(A) = P(B) + P(A) \cdot P(B)$.$2P(A) = P(B)(1 + P(A))$.$P(B) = \frac{2P(A)}{1 + P(A)}$.Given $P(A) = \frac{1}{4}$,we substitute the value:$P(B) = \frac{2 	imes \frac{1}{4}}{1 + \frac{1}{4}} = \frac{\frac{1}{2}}{\frac{5}{4}} = \frac{1}{2} 	imes \frac{4}{5} = \frac{2}{5}$.

$A$ and $B$ are independent events with $P(A)=\frac{1}{4}$ and $P(A \cup B)=2 P(B)-P(A)$,then $P(B)$ is

Similar Questions

If $A$ and $B$ are two independent events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{1}{5}$,then which of the following is true?

Let $S=\left\{E, E_{2} \ldots . E_{8}\right\}$ be a sample space of random experiment such that $P\left(E_{n}\right)=\frac{n}{36}$ for every $n =1,2 \ldots .$. Then the number of elements in the set $\left\{ A \subset S : P ( A ) \geq \frac{4}{5}\right\}$ is

$12$ balls are distributed among $3$ boxes. The probability that the first box will contain exactly $3$ balls is:

Consider a system of equations $ax + by = 0$ and $cx + dy = 0$,where $a, b, c, d \in \{0, 1\}$.
Statement $-1$: The probability that the system of equations has a solution is $1$.
Statement $-2$: The probability that the system of equations has a unique solution is $\frac{3}{8}$.

$A$ six-faced die is biased such that it is twice as likely to show an even number as an odd number when thrown. If the die is thrown twice,what is the probability that the sum of the two numbers obtained is even?

Vedclass Test Series

Exam Paper Generator

Online Exam Module