jee-advanced 2017 Q43

jee-advanced · India · paper1 Conditional Probability Direct Conditional Probability Computation from Definitions

Let $X$ and $Y$ be two events such that $P(X) = \frac{1}{3}$, $P(X \mid Y) = \frac{1}{2}$ and $P(Y \mid X) = \frac{2}{5}$. Then
[A] $P(Y) = \frac{4}{15}$
[B] $P(X' \mid Y) = \frac{1}{2}$
[C] $P(X \cap Y) = \frac{1}{5}$
[D] $P(X \cup Y) = \frac{2}{5}$

Let $X$ and $Y$ be two events such that $P(X) = \frac{1}{3}$, $P(X \mid Y) = \frac{1}{2}$ and $P(Y \mid X) = \frac{2}{5}$. Then

[A] $P(Y) = \frac{4}{15}$

[B] $P(X' \mid Y) = \frac{1}{2}$

[C] $P(X \cap Y) = \frac{1}{5}$

[D] $P(X \cup Y) = \frac{2}{5}$

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