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 :

Question

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

Solution

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