GATE 2021 ST – Question 24

Probability · Events and Conditional Probability · 1 mark · Numerical answer

Events A,B satisfy P(B)=3/4 and P(A∪Bᶜ)=1/2. If A and B are independent,find P(A),to two decimals.

Show answer and explanation

Correct answer: 0.32 to 0.35

Explanation

Let p=P A. Independence also holds with Bᶜ,so P(A∪Bᶜ)=p+1/4−p/4=1/4+3p/4. Equating to 1/2 gives p=1/3,rounded **0.33**.

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