To find the probabilities, we need to determine the total number of M&M's in the bag and then find the number of favorable outcomes for each event.

First, let's calculate the total number of M&M's:

5 \text{ (red)} + 7 \text{ (green)} + 8 \text{ (blue)} + 3 \text{ (yellow)} = 23 \text{ M&M's}

Now, let's calculate each probability.

1) Probability of picking a yellow M&M

There are 3 yellow M&M's out of 23 total M&M's. The probability $P(\text{yellow})$ is:

P(\text{yellow}) = \frac{\text{number of yellow M&M's}}{\text{total number of M&M's}} = \frac{3}{23}

2) Probability of picking a blue or green M&M

There are 8 blue and 7 green M&M's, so the number of blue or green M&M's is:

$8 \text{ (blue)} + 7 \text{ (green)} = 15$

The probability $P(\text{blue or green})$ is:

P(\text{blue or green}) = \frac{\text{number of blue or green M&M's}}{\text{total number of M&M's}} = \frac{15}{23}

3) Probability of picking an orange M&M

There are no orange M&M's in the bag. The probability $P(\text{orange})$ is:

P(\text{orange}) = \frac{\text{number of orange M&M's}}{\text{total number of M&M's}} = \frac{0}{23} = 0

To summarize:

1. The probability of picking a yellow M&M is $\frac{3}{23}$.
2. The probability of picking a blue or green M&M is $\frac{15}{23}$.
3. The probability of picking an orange M&M is 0.

If you have any further questions or need more details, feel free to ask.

Here are 8 related questions you might find interesting:

1. What is the probability of picking a red M&M?
2. What is the probability of picking a green M&M?
3. What is the probability of picking a blue M&M?
4. If one M&M is picked and not replaced, what is the probability of picking a yellow M&M on the second draw?
5. If one M&M is picked and not replaced, what is the probability of picking a red M&M on the second draw?
6. What is the probability of picking either a red or yellow M&M?
7. If one M&M is picked and replaced, what is the probability of picking two green M&M's in a row?
8. If two M&M's are picked at once, what is the probability that both are blue?

Tip: When calculating probabilities, always make sure your total number of possible outcomes is accurate, and reduce fractions to their simplest form for clarity.