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UPSC NDA I 2025 Mathematics Paper

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Question : 115 of 120

Marks: +1, -0

If

P(A)=1/3,P(B)=1/2

P(A∩B)=1/4

, then what is the value of

P(A | B^{C})

?

$1/8$
$3/8$
$5/8$
$7/8$

Solution:

Concept:

Conditional probability with a complement event uses the formula:

P(B | A^{C}) = \frac{P(B) - P(A \cap B)}{1 - P(A)}.

Explanation:

First, calculate the numerator:

P(B) - P(A \cap B) = \frac{1}{2} - \frac{1}{4} = \frac{1}{4}

.

Next, calculate the denominator:

1 - P(A) = 1 - \frac{1}{3} = \frac{2}{3}

.

Then, divide:

P(B | A^{C}) = \frac{1/4}{2/3} = \frac{1}{4} \times \frac{3}{2} = \frac{3}{8}

.

Answer:

Option B:

\frac{3}{8}

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