What is the probability that a positive integer selected at random from the set of positive integers not exceeding 100 is divisible by 2 or 5?
Let A : the event an integer < 100 divisible by 2
Let B the event an integer < 100 divisible by 5
then you need P(AUB) =?
REMEMBER P(AUB) = P(A)+P(B)-P(A+B)... FIND P(A) P(B) AND P(A+B) .....
THE REST IS EASY
There are, of course, 100 "positive integers not exceeding 100". HALF of those, 100/2= 50, are divisible by 2. 20 of them, 100/5= 20, are divisible by 5. 10 of them, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, are both divisible by 2 and divisible by 5 and we don't want to count them twice. Just "50+ 20" would be counting them twice so we need to subtract once: 50+ 20- 10= 60 are "divisible by 2 or 5"