JEE MAIN - Mathematics (2022 - 28th July Evening Shift - No. 14)
Let $$\mathrm{A}$$ and $$\mathrm{B}$$ be two events such that $$P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$$ and $$P(A \cap B)=\frac{1}{9} \cdot$$ Consider
(S1) $$P\left(A^{\prime} \cup B\right)=\frac{5}{6}$$,
(S2) $$P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{18}$$
Then :
Both (S1) and (S2) are true
Both (S1) and (S2) are false
Only (S1) is true
Only (S2) is true
Explanation
$$P(A/B) = {1 \over 7} \Rightarrow {{P(A \cap B)} \over {P(B)}} = {1 \over 7}$$
$$ \Rightarrow P(B) = {7 \over 9}$$
$$P(B/A) = {2 \over 5} \Rightarrow {{P(A \cap B)} \over {P(A)}} = {2 \over 5}$$
$$P(A) = {5 \over 2}\,.\,{1 \over 9} = {5 \over {18}}$$
$$S2:P(A' \cap B') = {1 \over {18}}$$
$$S1:$$ and $$P(A' \cup B) = {1 \over 9} + {6 \over 9} + {1 \over {18}} = {5 \over 6}.$$
Comments (0)
