It is given that the events A and B are such that P(A)=14, P(A/B)=12 and P(B/A)=23. Then, P(B) is

It is given that the events $A$ and $B$ are such that $P (A) = \frac{1}{4}, P (A / B) = \frac{1}{2}$ and $P (B / A) = \frac{2}{3} .$ Then, $P (B)$ is

A
$\frac{2}{3}$
B
$\frac{1}{2}$
C
$\frac{1}{6}$
D
$\frac{1}{3}$

Solution:

We have,

$\begin{array}{l} P (A \cap B) = P (A) P (B / A) \\ ∴ P (A \cap B) = \frac{1}{4} \times \frac{2}{3} = \frac{1}{6} \end{array}$

Now, $P (A / B) = \frac{P (A \cap B)}{P (B)} \Rightarrow \frac{1}{2} = \frac{1}{6} \times \frac{1}{P (B)} \Rightarrow P (B) = \frac{1}{3}$

Related content

Appreciation Words

Wave Optics Mind Map

Alternating Current Mind Map for Class 12, JEE & NEET

Paramedical Courses After Class 10

Top Courses After 12th Science with PCM, PCB and PCMB

Subject Change Application in School and College

CBSE Class 10 Result 2024: Is the Release Date Early? Check Expected Schedule

Mizoram NEET Merit List 2023

Government Jobs After 12th Arts Stream

Chhattisgarh NEET UG Merit List 2023