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The question in the image deals with probability. Let's break it down:

There are 45 students in total:
- 19 men
- 26 women
- 4 men received an A
- 5 women received an A

### Part (a)
**Find the probability that the student is a woman.**

\[
P(\text{woman}) = \frac{\text{number of women}}{\text{total number of students}} = \frac{26}{45}
\]

### Part (b)
**Find the probability that the student received an A.**

\[
P(\text{received an A}) = \frac{\text{total number of students who received an A}}{\text{total number of students}} = \frac{4 + 5}{45} = \frac{9}{45} = \frac{1}{5}
\]

### Part (c)
**Find the probability that the student is a woman or received an A.**

For this, we use the formula for the union of two events:

\[
P(\text{woman or A}) = P(\text{woman}) + P(\text{A}) - P(\text{woman and A})
\]

We already have:
\[
P(\text{woman}) = \frac{26}{45}, \quad P(\text{A}) = \frac{9}{45}
\]

Now, find \( P(\text{woman and A}) \), which is the probability that a student is a woman who received an A:

\[
P(\text{woman and A}) = \frac{5}{45}
\]

Now apply the formula:

\[
P(\text{woman or A}) = \frac{26}{45} + \frac{9}{45} - \frac{5}{45} = \frac{30}{45} = \frac{2}{3}
\]

### Part (d)
**Find the probability that the student did not receive an A.**

\[
P(\text{not A}) = 1 - P(\text{A}) = 1 - \frac{1}{5} = \frac{4}{5}
\]

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Do you want more details or have any questions about this solution? Here are some related questions to consider:

1. What is the probability that the student is a man?
2. What is the probability that the student is a man and did not receive an A?
3. How would you calculate the probability that the student is a woman and did not receive an A?
4. What is the probability that a randomly selected man received an A?
5. How does the probability change if more students receive A’s in future tests?

**Tip:** When calculating probabilities involving "or," always remember to subtract the overlap (students belonging to both categories).

In a statistics class of 45 students, there were 19 men and 26 women. Four of the men and five of the women received an A in the course. A student is chosen at random from the class. Find the probabilities for the following: (a) The student is a woman, (b) The student received an A, (c) The student is a woman or received an A, (d) The student did not receive an A.

Learn how to calculate probabilities in a statistics class of 45 students, with 19 men and 26 women. Explore various probability questions, such as the chance of selecting a woman or a student who received an A. This problem covers key statistical concepts and probability formulas.

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