A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a red ball or a non-green ball?

Given:

• Number of red balls = 5
• Number of blue balls = 3
• Number of green balls = 2

Step 1: Calculate the total number of balls in the bag.

$$\text{Total balls} = 5 + 3 + 2 = 10$$

i) Find the probability that the ball drawn is red.
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.

$$\text{P(Red)} = \frac{\text{Number of red balls}}{\text{Total number of balls}}$$ $$\text{P(Red)} = \frac{5}{10}$$ $$\text{P(Red)} = \frac{1}{2}$$

The probability that the ball drawn is red is $\boxed{\frac{1}{2}}$.

ii) Find the probability that the ball drawn is not green.
A ball that is not green can either be red or blue.

$$\text{Number of non-green balls} = \text{Number of red balls} + \text{Number of blue balls}$$ $$\text{Number of non-green balls} = 5 + 3 = 8$$ $$\text{P(Not Green)} = \frac{\text{Number of non-green balls}}{\text{Total number of balls}}$$ $$\text{P(Not Green)} = \frac{8}{10}$$ $$\text{P(Not Green)} = \frac{4}{5}$$

The probability that the ball drawn is not green is $\boxed{\frac{4}{5}}$.