Question

Out of $20$ consecutive integers, two are chosen at random. The probability that their sum is odd is

• A. $\frac{1}{9}$
• B. $\frac{2}{19}$
• C. $\frac{10}{19}$
• D. $\frac{7}{19}$

Answer 1

The correct option is C $\frac{10}{19}$

Out of twenty consecutive numbers there are $10$ even and $10$ odd numbers.
As a sum of two integers is odd if exactly one of them is
odd, otherwise it is even.
Let each number can only be chosen once.
If the first number is an even number, then other must be odd number
$\therefore$ Required probability $\Rightarrow \frac{{}^{10}{C}_1\times {}^{10}{C}_1}{{}^{20}{C}_2}=\frac{10}{19}$