Divisible by Two or Five

Apply inclusion-exclusion to the events of being divisible by 2 and by 5.

Subtract the overlap of numbers divisible by both, which are divisible by 10.

1. 1. Count each set

   Among $1$ through $100$ there are $50$ multiples of $2$, $20$ multiples of $5$, and $10$ multiples of $10$.

   $$|A\cup B|=50+20-10=60$$

2. 2. Compute the probability

   Divide the favorable count by $100$.

   $$P=\frac{60}{100}=\frac{3}{5}$$

Answer: 3/5