JEE PYQ: Probability Question 16
Question 16 - 2020 (02 Sep Shift 2)
Let $E^C$ denote the complement of an event $E$. Let $E_1$, $E_2$ and $E_3$ be any pairwise independent events with $P(E_i) > 0$ and $P(E_1 \cap E_2 \cap E_3) = 0$. Then $P(E_2^C \cap E_3^C / E_1)$ is equal to:
(1) $P(E_2^C) + P(E_3)$
(2) $P(E_3^C) - P(E_2^C)$
(3) $P(E_3) - P(E_2^C)$
(4) $P(E_3^C) - P(E_2)$
Show Answer
Answer: (4)
Solution
$P\left(\frac{E_2^C \cap E_3^C}{E_1}\right) = \frac{P(E_1) - P(E_1 \cap E_2) - P(E_1 \cap E_3) + 0}{P(E_1)} = 1 - P(E_2) - P(E_3) = P(E_3^C) - P(E_2)$.
BETA
