If P(A) = 0.3 , P(B) = 0.4 and P(A|B) = 0.5 , then what is the value of P(B|A) ?

Correct answer: D. 0.667 Given P(A) = 0.3 , P(B) = 0.4 and P(A|B) = 0.5 . Using the formula for conditional probability: P(A|B) = (P(A B))/(P(B)) 0.5 = (P(A B))/(0.4) P(A B) = 0.5 × 0.4 = 0.2 Now, finding P(B|A) : P(B|A) = (P(A B))/(P(A)) P(B|A) = (0.2)/(0.3) = (2)/(3) 0.667 Answer: 0.667

NDA 2025

Exam: NDA
Year: 2025
Subject: Mathematics
Chapter: Probability

NDA 2025 · Mathematics · Probability

If P(A) = 0.3 , P(B) = 0.4 and P(A|B) = 0.5 , then what is the...

P(A) = 0.3

P(B) = 0.4

and

P(A|B) = 0.5

, then what is the value of

P(B|A)

Options

A $0.325$
B $0.333$
C $0.375$
D $0.667$

Correct answer

D. $0.667$

Step-by-step solution

Given

P(A) = 0.3

P(B) = 0.4

and

P(A|B) = 0.5

.

Using the formula for conditional probability:

P(A|B) = \dfrac{P(A \cap B)}{P(B)}

0.5 = \dfrac{P(A \cap B)}{0.4}

P(A \cap B) = 0.5 \times 0.4 = 0.2

Now, finding

P(B|A)

P(B|A) = \dfrac{P(A \cap B)}{P(A)}

P(B|A) = \dfrac{0.2}{0.3} = \dfrac{2}{3} \approx 0.667

Answer:

0.667

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