Question

A box contains 11 tickets numbered from 1 to 11 . Six tickets are drawn simultaneously at random. Let $E_1$ denotes the event that the sum of the numbers on the tickets drawn is even and $E_2$ denotes the event that the sum of the numbers on the tickets drawn is odd Which of the following hold good?

• A. $E _1$ and $E _2$ are equally likely
• B. $E _1$ and $E _2$ are exhaustive
• C. $P \left( E _2\right)> P \left( E _1\right)$
• D. $P\left(E_1 / E_2\right)^*=P\left(E_2 / E_1\right)$

Answer 1

Answer: (B), (C), (D)

$P\left(E_2\right)=\frac{118}{231}$ and $P\left(E_1\right)=\frac{113}{231} ; S=\{1,2,3,4,5,6,7,8,9,10,11\}$
$E _2 \Rightarrow 1$ odd +5 even or 3 odd +3 even
or 5 odd + one even
as $P\left(E_1 \cap E_2\right)=0 \Rightarrow P\left(E_1 / E_2\right)=P\left(E_2 / E_1\right)=0$