If I pick a number anywhere from 1 to 1000 at random, what is the probability that the number is   divisible by either 2 or 5?

60%. Half ot the numbers will be divisible by two. There are ten numbers divisible by 5 in each 100 (odd multiples of 5) so there are 100 of those from 1 to 1000. 600/1000 =0.6 or 60%.

To derive the equation we need, think of a deck of card.  the probablity of a heart or a king.

There are 13 hears in a deck and 4 kings, but we just now counted the king of hearts twice, so we have to take out the one card that's both.

So:

P(A or B) = P(A) + P(B) - P(A and B)

The probability of a number being divisible by 2:  1/2

The probability of a number being divisible by 5:  1/5

The probability of a number being divisible by both 2 and 5 (aka 10): 1/10

Now we can substitute these probabilities into the equation and simplify:

1/2 + 1/5 - 1/10

5/10 + 2/10 - 1/10

(5 + 2 - 1)/10

6/10

3/5

Since 2 x 5 = 10 and 1000 is a multiple of 10, all we have to do is inspect the numbers 1 to 10 because every next 10 will repeat the pattern of 2 and 5 divisibility.

1 (2) 3 (4) (5) (6) 7 (8) 9 (10)

So p = 0.6