Consider three sets E₁={1,2,3}, F₁={1,3,4} and G₁={2,3,4,5} . Two elements are chosen at rando

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14.Probability

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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 $E_2=E_1-S_1$ 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 $G _2= G _1 \cup S _2$. Finally, two elements are chosen at random, without replacement, from the set $G _2$ and let $S _3$ denote the set of these chosen elements.

Let $E_3=E_2 \cup S_3$. Given that $E_1=E_3$, let $p$ be the conditional probability of the event $S_1=\{1,2\}$. Then the value of $p$ is

A

$\frac{1}{5}$

B

$\frac{3}{5}$

C

$\frac{1}{2}$

D

$\frac{2}{5}$

(IIT-2021)

Solution

Standard 11

Mathematics

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