jee-advanced 2021 Q3

jee-advanced · India · paper1 3 marks Conditional Probability Sequential/Multi-Stage Conditional Probability
Consider three sets $E_1 = \{1,2,3\}$, $F_1 = \{1,3,4\}$ and $G_1 = \{2,3,4,5\}$. Two elements are chosen at random, without replacement, from the set $E_1$, and let $S_1$ denote the set of these chosen elements. Let $E_2 = E_1 \setminus S_1$ and $F_2 = F_1 \cup S_1$. Now two elements are chosen at random, without replacement, from the set $F_2$ and let $S_2$ denote the set of these chosen elements.
Let $G_2 = G_1 \cup S_2$. The value of $P(E_2 = F_2)$ is
(A) $\frac{1}{7}$
(B) $\frac{3}{7}$
(C) $\frac{1}{5}$
(D) $\frac{2}{7}$
Consider three sets $E_1 = \{1,2,3\}$, $F_1 = \{1,3,4\}$ and $G_1 = \{2,3,4,5\}$. Two elements are chosen at random, without replacement, from the set $E_1$, and let $S_1$ denote the set of these chosen elements. Let $E_2 = E_1 \setminus S_1$ and $F_2 = F_1 \cup S_1$. Now two elements are chosen at random, without replacement, from the set $F_2$ and let $S_2$ denote the set of these chosen elements.

Let $G_2 = G_1 \cup S_2$. The value of $P(E_2 = F_2)$ is

(A) $\frac{1}{7}$

(B) $\frac{3}{7}$

(C) $\frac{1}{5}$

(D) $\frac{2}{7}$