WBJEE · Maths · Probability
Let \(A\) and \(B\) are two independent events. The probability that both \(A\) and \(B\) happen is \(\frac{1}{12}\) and probability that neither A nor \(B\) happen is \(\frac{1}{2}\). Then
- A \(P(A)=\frac{1}{3}, P(B)=\frac{1}{4}\)
- B \(P(A)=\frac{1}{2}, P(B)=\frac{1}{6}\)
- C \(P(A)=\frac{1}{6}, P(B)=\frac{1}{2}\)
- D \(P(A)=\frac{2}{3}, P(B)=\frac{1}{8}\)
Answer & Solution
Correct Answer
(A) \(P(A)=\frac{1}{3}, P(B)=\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{ll} \text {Hint : } P(A \cap B)=\frac{1}{12} & \Rightarrow P(A) P(B)=\frac{1}{12} \cdots (1) \\ P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{2} & \Rightarrow P(A \cup B)=1-\frac{1}{2}=\frac{1}{2} \end{array}\)…
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