NDA 2024 Maths · Mathematics · Probability · easy

If A and B are independent events with P(A)=1/3 and P(B)=1/4, then P(A∪ B) is equal to

Single correct option

A

and

B

are independent events with

P(A)=\frac13

and

P(B)=\frac14

, then

P(A\cup B)

is equal to

Show answer and solution

Answer: (C) $\frac12$

Independence gives

P(A\cap B)=\frac13\cdot\frac14=\frac1{12}

. Then

P(A\cup B)=\frac13+\frac14-\frac1{12}=\frac{4+3-1}{12}=\frac12

. Trap:

\frac7{12}

P(A)+P(B)

without subtracting the overlap, and

\frac1{12}

is the intersection.

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