**College Degrees Awarded** The table below represents the college degrees awarded in a recent academic year by gender.

**Bachelor's**

**Master's**

**Doctorate**

**Men**

726,866

272,761

27,768

**Women**

736,323

292,003

27,562

Choose a degree at random. Find the probabilities of the following. Express your answer as a fraction or a decimal rounded to three decimal places.

What is the probability that the degree was a master's degree or a degree awarded to a men?

*P*master's degree

To solve the problem of finding the probability of selecting either a master's degree or a degree awarded to men, we can use the following formula for the union of two events, \( A \) (master's degree) and \( B \) (degree awarded to men):

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

### Step 1: Calculate the total number of degrees awarded.
The total number of degrees awarded is the sum of all bachelor's, master's, and doctorate degrees for both men and women:

\[
\text{Total Degrees} = 726,866 + 736,323 + 272,761 + 292,003 + 27,768 + 27,562 = 2,083,283
\]

### Step 2: Define the events.

- Event \( A \): The degree is a master's degree.
- Event \( B \): The degree is awarded to a man.

Now, let's calculate each probability.

### Step 3: Calculate \( P(A) \) (Probability of a master's degree).
The total number of master's degrees awarded is:

\[
272,761 + 292,003 = 564,764
\]

So, the probability of a master's degree, \( P(A) \), is:

\[
P(A) = \frac{564,764}{2,083,283} \approx 0.271
\]

### Step 4: Calculate \( P(B) \) (Probability of a degree awarded to men).
The total number of degrees awarded to men is:

\[
726,866 + 272,761 + 27,768 = 1,027,395
\]

So, the probability of a degree awarded to a man, \( P(B) \), is:

\[
P(B) = \frac{1,027,395}{2,083,283} \approx 0.493
\]

### Step 5: Calculate \( P(A \cap B) \) (Probability of a master's degree awarded to a man).
The number of master's degrees awarded to men is:

\[
272,761
\]

So, \( P(A \cap B) \) is:

\[
P(A \cap B) = \frac{272,761}{2,083,283} \approx 0.131
\]

### Step 6: Apply the formula for the union of two events.

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]
\[
P(A \cup B) = 0.271 + 0.493 - 0.131 = 0.633
\]

Thus, the probability that the degree was a master's degree or a degree awarded to men is approximately:

\[
\boxed{0.633}
\]

Would you like more details on any of these steps?

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Here are 5 related questions:
1. What is the probability of randomly selecting a bachelor's degree?
2. What is the probability of selecting a doctorate degree?
3. What is the probability of selecting a degree awarded to women?
4. What is the probability of selecting a doctorate degree awarded to women?
5. What is the probability of selecting a master's degree awarded to women?

**Tip:** In probability problems involving "or" (union), always check for any overlap between the two events to avoid double counting.

Choose a degree at random. Find the probabilities of the following. Express your answer as a fraction or a decimal rounded to three decimal places. What is the probability that the degree was a master's degree or a degree awarded to men?

Calculate the probability of selecting either a master's degree or a degree awarded to men using the union rule of probability. This problem involves determining event probabilities from given data on college degrees awarded by gender, suitable for Grades 10-12 students.

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