QJEEM22Mab780: JEE Main 2022 Mathematics - Class 12 JEEM22Mab780 Solution: If and are two events such that and , then is equal to :

$P(A) = {1 \over 3},\,P(B) = {1 \over 5}$ and $P\left( {A \cup B} \right) = {1 \over 2}$

$\therefore$ $P\left( {A \cap B} \right) = {1 \over 3} + {1 \over 5} - {1 \over 2} = {1 \over {30}}$

Now, $P\left( {A|B'} \right) + P\left( {B|A'} \right) = {{P\left( {A \cap B'} \right)} \over {P\left( {B'} \right)}} + {{P\left( {B \cap A'} \right)} \over {P\left( {A'} \right)}}$

$= {{{9 \over {30}}} \over {{4 \over 5}}} + {{{5 \over {30}}} \over {{2 \over 3}}} = {5 \over 8}$