Tj, let's think about this. The only way to get an odd sum is with one even and one odd number picked. Let's start with that.
1-10 has a total of 5 even numbers and 5 odd numbers. For each of my 5 evens, there are 5 different possibilities of my friend picking odd. That's 5 x 5 = 25 possibilities.
However, if I roll an odd, one of the five, there are also five ways my friend can roll an even. That's another 25 ways, for a total of 50.
How many possibilities are there altogether? I have 10 numbers to choose from, and so does my friend. 10 x 10 = 100.
The probability of the sum being odd is then 50/100, or 1/2.
