Question

A box contains $100$ tickets numbered $1,2,.....,100$. Two tickets are chosen at random. It is given that the minimum number on the two chosen tickets is not more than $10$. The maximum number on them is $5$ with probability.....

• A. $\frac{1}{9}$
• B. $\frac{1}{4}$
• C. $\frac{1}{90}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A $\frac{1}{9}$

Let $A$ be the event that the maximum number on the two chosen tickets is not more than $10$, and B be the event that the maximum number on them is $5.$
$\therefore P(A\cap B)=\frac{{}^5{C}_1}{{}^{100}{C}_2}$ and $P\left(A\right)=\frac{{}^{10}{C}_2}{{}^{100}{C}_2}$
Then $P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{{}^5{C}_1}{{}^{10}{C}_2}=\frac{1}{9}$