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Choose the correct answer in the following Question 17 and 18:Two events $A$ and $B$ are said to be independent, if
(a) $A$ and $B$ are mutually exclusive
(b) $\quad \mathbf{P}\left(\mathrm{A}^{\prime} \mathbf{B}^{\prime}\right)=[1-\mathbf{P}(\mathrm{A})][1-\mathrm{P}(\mathrm{B})]$
(c) $\mathbf{P}(\mathrm{A})=\mathbf{P}(\mathrm{B})$
(d) $P(A)+P(B)=1$
(a) $A$ and $B$ are mutually exclusive
(b) $\quad \mathbf{P}\left(\mathrm{A}^{\prime} \mathbf{B}^{\prime}\right)=[1-\mathbf{P}(\mathrm{A})][1-\mathrm{P}(\mathrm{B})]$
(c) $\mathbf{P}(\mathrm{A})=\mathbf{P}(\mathrm{B})$
(d) $P(A)+P(B)=1$
Solution:
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Verified Answer
(b) $P\left(A^{\prime}\right.$ and $\left.B^{\prime}\right)=[1-P(A)] \cdot\left[1-P(B)=P\left(A^{\prime}\right) \cdot P\left(B^{\prime}\right)\right.$ Thus option (b) is correct.
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