A bag contains 20 red caps and 10 green caps. One cap is drawn out of the bag. What is the probability that it is: a) a red cap? b) a green cap?

The bag contains 20 red caps and 10 green caps.
Total number of caps = Number of red caps + Number of green caps

$$\text{Total caps} = 20 + 10 = 30$$

The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
Number of red caps = 20
Total number of caps = 30

$$P(\text{red cap}) = \frac{\text{Number of red caps}}{\text{Total number of caps}} = \frac{20}{30}$$

Simplify the fraction:

$$P(\text{red cap}) = \frac{2}{3}$$

The probability of drawing a red cap is $\boxed{\frac{2}{3}}$.

Number of green caps = 10
Total number of caps = 30

$$P(\text{green cap}) = \frac{\text{Number of green caps}}{\text{Total number of caps}} = \frac{10}{30}$$

Simplify the fraction:

$$P(\text{green cap}) = \frac{1}{3}$$

The probability of drawing a green cap is $\boxed{\frac{1}{3}}$.