Question

If events A and B are such that \(P(A) = \frac{1}{4}\), \(P(A\cap B) = \frac{1}{10}\) and \(P(A/B) = 2P(B/A)\) then \(P(B) =\)...........

• A. \(\frac{1}{2}\)
• B. \(\frac{1}{5}\)
• C. \(\frac{1}{8}\)
• D. \(\frac{2}{5}\)

Hint:

Write both conditional probabilities with P(A and B) and compare.

Answer 1

The Correct Option is C

Step 1: Compute using values:
$P(B/A)=\dfrac{1/10}{1/4}=\dfrac25$. So $P(A/B)=2\cdot\dfrac25=\dfrac45$.

Step 2: Find P(B):
$P(A/B)=\dfrac{P(A\cap B)}{P(B)}$, so $P(B)=\dfrac{1/10}{4/5}=\dfrac{1}{10}\cdot\dfrac54=\dfrac18$.

Step 3: Pick:
Option C.

Final Answer:
The relation gives P(A) = 2 P(B), so P(B) = 1/8. \[ \boxed{\text{(C) }\dfrac18} \]