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Home » If and are events such that and , then and areA. IndependentB. Mutually exclusiveC. Both ‘ ‘ and ‘ .’D. None of these
If A and B are events such that P(A)=\frac{1}{2}, P(B)=\frac{7}{12} and P\left(A^{\prime} \cup B^{\prime}\right)=\frac{1}{4}, then A and B are
A. Independent
B. Mutually exclusive
C. Both ‘ a ‘ and ‘ b.’
D. None of these
Binomial Distribution | CBSE | Class 12 | Exercise 32A | Maths | RS Aggarwal
If A and B are events such that P(A)=\frac{1}{2}, P(B)=\frac{7}{12} and P\left(A^{\prime} \cup B^{\prime}\right)=\frac{1}{4}, then A and B are
A. Independent
B. Mutually exclusive
C. Both ‘ a ‘ and ‘ b.’
D. None of these

We are having two events A and B such that
\begin{array}{l} P(A)=\frac{1}{2}, P(B)=\frac{7}{12} \text { and } P\left(A^{\prime} \cup B^{\prime}\right)=\frac{1}{4} \\ P\left(A^{\prime} \cup B^{\prime}\right)=P^{\prime}(A \cap B)=1-P(A \cap B)=\frac{1}{4} \\ \Rightarrow P(A \cap B)=\frac{3}{4} \end{array}
\Rightarrow As P(A \cap B) \neq P(A) \cdot P(B) \ldots thus, they are not independent,
\Rightarrow And as P(A \cup B) \neq P(A)+P(B) \ldots thus, they are not mutually exclusive.
Hence, the answer is option d.

i

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