If P(A) = 3/(10), P(B) = 2/5 and P(A ∪ B) = 3/5, then the value of P(A|B) + P(B|A) is:

If $P(A) = \dfrac{3}{10},\ P(B) = \dfrac{2}{5}$ and $P(A \cup B) = \dfrac{3}{5}$, then the value of $P(A|B) + P(B|A)$ is:

(a)$\dfrac{1}{12}$
(b)$\dfrac{7}{12}$
(c)$\dfrac{1}{10}$
(d)$\dfrac{1}{3}$

Open in the Venn diagram generator and visualiser

Answer

Correct option: (b)

Answer: (b) $\dfrac{7}{12}$ $P(A \cap B) = P(A) + P(B) - P(A \cup B) = \dfrac{3}{10} + \dfrac{2}{5} - \dfrac{3}{5} = \dfrac{1}{10}$. $P(A|B) = \dfrac{1/10}{2/5} = \dfrac{1}{4}$ and $P(B|A) = \dfrac{1/10}{3/10} = \dfrac{1}{3}$, so the sum is $\dfrac{1}{4} + \dfrac{1}{3} = \dfrac{7}{12}$.