https://file.aiquickdraw.com/mathbot/file/172591535493688w4kmx4.jpg

Let's break down the problem from the image into two parts and solve it.

### Part (a) - Theoretical Probability of Getting a Reward:
The problem states that the monkey gets a reward if it chooses any shape **that is not red**. So, to calculate the theoretical probability of getting a reward, we need to determine:
- Total number of shapes.
- Total number of red shapes (since the monkey doesn't get a reward when choosing red).

From the image:
- Total number of shapes = 24.
- Number of red shapes = 5 (all red shapes are triangles and stars).

So, the number of shapes that are **not red** (i.e., shapes that will result in a reward) = Total shapes - Red shapes = 24 - 5 = 19.

The theoretical probability \( P(\text{Reward}) \) is the ratio of non-red shapes to total shapes:

\[
P(\text{Reward}) = \frac{19}{24}
\]

### Part (b) - Theoretical Probability of Not Choosing a Star:
Next, we need to find the probability that the monkey does **not** choose a star. To calculate this:
- Total number of stars = 7 (there are red, yellow, green, and blue stars).
- Number of non-star shapes = Total shapes - Stars = 24 - 7 = 17.

The theoretical probability \( P(\text{Not a Star}) \) is the ratio of non-star shapes to total shapes:

\[
P(\text{Not a Star}) = \frac{17}{24}
\]

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### Final Answers:
- **(a)** The theoretical probability of the monkey getting a reward is \( \frac{19}{24} \).
- **(b)** The theoretical probability that the monkey does not choose a star is \( \frac{17}{24} \).

Would you like more details on any of the steps, or do you have other questions? Here are some related questions to explore:

1. What is the probability of the monkey choosing a red star?
2. What is the probability of choosing a yellow shape?
3. How would the probability change if another red shape is added?
4. What is the complement of the probability that the monkey chooses a star?
5. How does this type of experiment relate to conditional probability?

**Tip:** Always remember that probability is the ratio of favorable outcomes to total possible outcomes.

In a lab study of learned behaviors, monkeys are taught to randomly choose a shape. The monkey is rewarded if the shape is not red. Determine the theoretical probability of the monkey being rewarded and the probability of not choosing a star.

Explore the probability problem involving a monkey randomly selecting shapes in a lab experiment. Calculate the theoretical probability of receiving a reward and the probability of not choosing a star. This problem helps understand basic probability concepts and ratios.

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