Question

A number is chosen at random from the positive, even integers from 2 to 50. Find the probability that the number chosen is divisible by 5 or 8.
1/25

2/5

11/25

Answer 1

There are 25 even integers between 2 and 50 (2,4,6,...,50).
Among them, there are 5 numbers divisible by 5 (10,20,30,40,50), 6 divisible by 8 (8,16,24,32,40,48), and 1 divisible by 5 and 8 simultaneously (40).

The last means these two events are not mutually exclusive. So, if

A - the event of choosing a number divisible by 5,
B - the event of choosing a number divisible by 8,

the probability of choosing a number divisible by 5 or 8 is equal to
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

So,
$P(A\cup B)=\dfrac{5}{25}+\dfrac{6}{25}-\dfrac{1}{25}\\ P(A\cup B)=\dfrac{10}{25}\\ \boxed{P(A\cup B)=\dfrac{2}{5}}$