Question

In a lottery $50$ tickets are sold in which $14$ are prizes. A man bought $2$ tickets, then the probability that the man win the prize is

• A. $\frac{17}{35}$
• B. $\frac{18}{35}$
• C. $\frac{72}{175}$
• D. $\frac{13}{175}$

Answer 1

The correct option is A

$\frac{17}{35}$

Explanation for the correct answer:

Find the probability that the man win the prize is:

Given,

Total number of tickets are $50$

A man bought $2$ tickets

Thus there are ${}^{50}{C}_2$ ways.

Out of $50$tickets, $14$ are prizes. Hence, there are $36$ blank tickets.
The probability that the $2$ tickets are blank is

$\begin{array}{rcl}P& =& \frac{{}^{36}{C}_2}{{}^{50}{C}_2}\\ & =& \frac{{\displaystyle \frac{36\times 35}{2}}}{{\displaystyle \frac{50\times 49}{2}}}\mathbf{[}{\mathbf{\because }}^{\mathbf{n}}{\mathbf{C}}_{\mathbf{r}}\mathbf{=}\frac{\mathbf{n}\mathbf{!}}{\mathbf{r}\mathbf{!}\mathbf{}\mathbf{(}\mathbf{n}\mathbf{-}\mathbf{r}\mathbf{)}\mathbf{!}}\mathbf{]}\\ & =& \frac{18}{35}\end{array}$

Therefore, the probability that man win the prize is,

$\begin{array}{rcl}1-P& =& 1-\frac{18}{35}\\ & =& \frac{17}{35}\end{array}$

Hence, the correct option is (A).