The question in the image asks about the probability of randomly choosing a blue marble from a bag containing 10 marbles: 3 blue marbles, 2 red marbles, and 5 yellow marbles. It specifies that the answer should be written as a fraction in its simplest form.

Solution:

1. Total marbles:
   The total number of marbles is:
   $3 \, \text{(blue)} + 2 \, \text{(red)} + 5 \, \text{(yellow)} = 10$

2. Number of blue marbles:
   The number of blue marbles is:
   $3$

3. Probability of selecting a blue marble:
   The probability is calculated as:
   $\text{Probability} = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{3}{10}$

Since $\frac{3}{10}$ is already in its simplest form, the final answer is:
$\boxed{\frac{3}{10}}$

Would you like a more detailed explanation or additional examples related to probability? Here are 5 related questions you might find interesting:

1. What is the probability of randomly choosing a red marble from the same bag?
2. What is the probability of randomly choosing a yellow marble?
3. If two marbles are drawn without replacement, what is the probability that both are blue?
4. What is the probability of choosing a marble that is not blue?
5. How would the probabilities change if an additional blue marble is added to the bag?

Tip: To calculate probability, always divide the favorable outcomes by the total possible outcomes!