Question

a spinner is numbered from 1 through 10 with each number equally likely to occur. what is the probability of obtaining a number less than 2 or greater than 7 in a single spin?

Answer 1

Less than 2: 1
More than 7: 8, 9, 10
So that's 4 possible ways.
There are 10 total possible ways.

4/10

Answer 2

P(X<2 OR X>7) = P(1) + P(2) + P(8)+P(9)+P(10)

you don't have to subtract away the probability of their intersections, since they are mutually exclusive events. there is never a probability that you will get the P(1 and 2) or something like that.