(A) Given that $A$ and $B$ are independent events. We know that $P(A) = 1 - P(A^{\prime})$ and $P(B) = 1 - P(B^{\prime})$. Given $P(A^{\prime}) = \fra

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(A) Given that $A$ and $B$ are independent events. We know that $P(A) = 1 - P(A^{\prime})$ and $P(B) = 1 - P(B^{\prime})$. Given $P(A^{\prime}) = \frac{2}{3}$,so $P(A) = 1 - \frac{2}{3} = \frac{1}{3}$. Given $P(B^{\prime}) = \frac{2}{7}$,so $P(B) = 1 - \frac{2}{7} = \frac{5}{7}$. Since $A$ and $B$ are independent,$P(A \cap B) = P(A) \cdot P(B)$. Therefore,$P(A \cap B) = \frac{1}{3} \cdot \frac{5}{7} = \frac{5}{21}$.

Class 11 Mathematics Probability Set Based probability

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If the events $A$ and $B$ are independent,and $P(A^{\prime}) = \frac{2}{3}$ and $P(B^{\prime}) = \frac{2}{7}$,then $P(A \cap B)$ is equal to:

KCET 2014 All KCET

A
$ \frac{5}{21} $
B
$ \frac{3}{21} $
C
$ \frac{4}{21} $
D
$ \frac{1}{21} $

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If the events $A$ and $B$ are independent,and $P(A^{\prime}) = \frac{2}{3}$ and $P(B^{\prime}) = \frac{2}{7}$,then $P(A \cap B)$ is equal to:

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