**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.

To find the probabilities, we will first calculate the total number of degrees awarded for each degree level (Bachelor's, Master's, Doctorate) and then compute the probabilities for each situation based on the gender and degree type.

### Step 1: Calculate the total number of degrees awarded
We will first sum up the total degrees awarded to men and women at each level:

- **Bachelor's Degrees Total**:  
  \[
  726,866 \,(\text{men}) + 736,323 \,(\text{women}) = 1,463,189
  \]
  
- **Master's Degrees Total**:  
  \[
  272,761 \,(\text{men}) + 292,003 \,(\text{women}) = 564,764
  \]

- **Doctorate Degrees Total**:  
  \[
  27,768 \,(\text{men}) + 27,562 \,(\text{women}) = 55,330
  \]

### Step 2: Calculate the overall total number of degrees
Now, let's find the total number of degrees awarded across all levels:

\[
1,463,189 \,(\text{Bachelor's}) + 564,764 \,(\text{Master's}) + 55,330 \,(\text{Doctorate}) = 2,083,283
\]

### Step 3: Compute the probabilities
Now that we have the total, let's find the probabilities for different scenarios:

#### 1. **The degree is a Bachelor's degree**:
The total number of Bachelor's degrees is 1,463,189. The probability is:

\[
P(\text{Bachelor's}) = \frac{1,463,189}{2,083,283} \approx 0.702
\]

#### 2. **The degree is a Master's degree**:
The total number of Master's degrees is 564,764. The probability is:

\[
P(\text{Master's}) = \frac{564,764}{2,083,283} \approx 0.271
\]

#### 3. **The degree is a Doctorate degree**:
The total number of Doctorate degrees is 55,330. The probability is:

\[
P(\text{Doctorate}) = \frac{55,330}{2,083,283} \approx 0.027
\]

#### 4. **The degree is awarded to a man**:
The total number of degrees awarded to men is:

\[
726,866 \,(\text{Bachelor's}) + 272,761 \,(\text{Master's}) + 27,768 \,(\text{Doctorate}) = 1,027,395
\]
So, the probability is:

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

#### 5. **The degree is awarded to a woman**:
The total number of degrees awarded to women is:

\[
736,323 \,(\text{Bachelor's}) + 292,003 \,(\text{Master's}) + 27,562 \,(\text{Doctorate}) = 1,055,888
\]
So, the probability is:

\[
P(\text{Woman}) = \frac{1,055,888}{2,083,283} \approx 0.507
\]

### Summary of probabilities:
1. Probability of a Bachelor's degree: **0.702**
2. Probability of a Master's degree: **0.271**
3. Probability of a Doctorate degree: **0.027**
4. Probability the degree is awarded to a man: **0.493**
5. Probability the degree is awarded to a woman: **0.507**

Would you like more details on any of these, or have any specific questions?

Here are some related questions:
1. What is the probability of a Bachelor's degree awarded to a woman?
2. What is the probability of a Master's degree awarded to a man?
3. What is the combined probability of a Doctorate degree awarded to either a man or a woman?
4. How would the probabilities change if the total number of Master's degrees increased?
5. What is the complement of the probability of a Bachelor's degree?

**Tip**: When calculating probabilities, ensure all possible outcomes are considered to confirm that the total probability sums to 1.

The table below represents the college degrees awarded in a recent academic year by gender. Choose a degree at random. Find the probabilities of the following: Bachelor's, Master's, Doctorate, awarded to a man, awarded to a woman.

Find the probability of different college degrees (Bachelor's, Master's, Doctorate) awarded by gender in a recent academic year. Learn how to calculate probabilities using fractions and decimals based on real data. Suitable for students in Grades 10-12.

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