If P(A) = (1)/(3) , P(B) = (1)/(2) and P(A B) = (1)/(4) , then what is the value of P(B | A^c) ?

Correct answer: B. (3)/(8) The conditional probability is given by: P(B | A^c) = (P(B A^c))/(P(A^c)) The probability of the complement of A is: P(A^c) = 1 - P(A) = 1 - (1)/(3) = (2)/(3) The probability of B A^c is: P(B A^c) = P(B) - P(A B) = (1)/(2) - (1)/(4) = (1)/(4) Substituting these values into the formula: P(B | A^c) = ((1)/(4))/((2)/(3)) = (3)/(8) Answer: (3)/(8)

NDA 2025

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

NDA 2025 · Mathematics · Probability

If P(A) = (1)/(3) , P(B) = (1)/(2) and P(A B) = (1)/(4) , then what...

P(A) = \dfrac{1}{3}

P(B) = \dfrac{1}{2}

and

P(A \cap B) = \dfrac{1}{4}

, then what is the value of

P(B | A^c)

Options

A $\dfrac{1}{8}$
B $\dfrac{3}{8}$
C $\dfrac{5}{8}$
D $\dfrac{7}{8}$

Correct answer

B. $\dfrac{3}{8}$

Step-by-step solution

The conditional probability is given by:

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

The probability of the complement of

A

is:

P(A^c) = 1 - P(A) = 1 - \dfrac{1}{3} = \dfrac{2}{3}

The probability of

B \cap A^c

is:

P(B \cap A^c) = P(B) - P(A \cap B) = \dfrac{1}{2} - \dfrac{1}{4} = \dfrac{1}{4}

Substituting these values into the formula:

P(B | A^c) = \dfrac{\dfrac{1}{4}}{\dfrac{2}{3}} = \dfrac{3}{8}

Answer:

\dfrac{3}{8}

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