Question

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

• A. $\frac{10}{19}$
• B. $\frac{1}{20}$
• C. $\frac{19}{20}$
• D. $\frac{9}{19}$

Answer 1

Answer: (A)

$\frac{10}{19}$

Answer 2

You have to choose Odd-Even or Even-Odd.
The probabilities of both events are the same: at the start there’s the same amount of odds and evens.
So calculate for one of them and multiply by 22.

First number being odd: $\frac{10}{20}=\frac{1}{2}$

Second number being even: $\frac{10}{19}$

Overall $=\frac{10}{19}\times2\times2=\frac{10}{19}$...
So the correct option is (A)