Question

From 1,2,3,..,20 if two natural numbers are selected, find the probability of getting both even if sum of the selected number is even.

Answer 1

From 1,2,3,..,20

Total number of even numbers=10

And total number of odd numbers=10

Two numbers are selected & if sum of the selected number is even then both the number must be either odd or even.

Ways to choose two odd numbers =${}^{10}{C}_2$

Ways to choose two even numbers =${}^{10}{C}_2$

Probability of getting both even if sum of the selected number is even=Ways to choose two even numbers/Total ways to choose number such that sum is even

=${}^{10}{C}_2$/(${}^{10}{C}_2$+${}^{10}{C}_2$)=1/2