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

Correct answer: D. 11/12 Using De Morgan's laws, P( A B) = 1 - P(A B ) P(A B ) = P(A) - P(A B) Substituting the given values: P(A B ) = (1)/(3) - (1)/(4) = (1)/(12) Therefore, P( A B) = 1 - (1)/(12) = (11)/(12) Answer: 11/12

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 is the...

P(A) = 1/3

P(B) = 1/2

and

P(A \cap B) = 1/4

, then what is the value of

P(\bar{A} \cup B)

Options

A $7/12$
B $2/3$
C $3/4$
D $11/12$

Correct answer

D. $11/12$

Step-by-step solution

Using De Morgan's laws,

P(\bar{A} \cup B) = 1 - P(A \cap \bar{B})

P(A \cap \bar{B}) = P(A) - P(A \cap B)

Substituting the given values:

P(A \cap \bar{B}) = \dfrac{1}{3} - \dfrac{1}{4} = \dfrac{1}{12}

Therefore,

P(\bar{A} \cup B) = 1 - \dfrac{1}{12} = \dfrac{11}{12}

Answer:

11/12

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