Question

In a lottery, there are 10 balls numbered 1 through 10. If you pick 2 balls at random, what is the probability you get a 2 and a 9? Is it 1/90 or 1/45?

Answer 1

The first ball can be either 2 or 9, which gives you 2 out of 10 => 2/10
The second on has to be "the other" from the one before which is 1 out the the 9 left: 1/9
p = 2/10 * 1/9 = 2 / 90 = 1/45

Answer 2

Right ok. So you basically do 1/10 x 1/9 + 1/10 x 1/9. So you assume that both 2 and 9 or 9 and 2 are possibilities?

Answer 3

Yes both ways work. You are using the tree approach which works just as fine!