Giving a test to a group of students, the table below summarizes the grade earned by gender.

A	B	C	Total
Male	8	9	18	35
Female	6	10	12	28
Total	14	19	30	63

If one student is chosen at random, find the probability that the student was not a female and did not earn grade C. Round your answer to four decimal places.

To find the probability that the randomly chosen student was not a female and did not earn a grade C, we need to first determine how many students meet both criteria (not female and not earning grade C).

### Step 1: Identify Relevant Groups
- **Not Female** means Male.
- **Not Grade C** means either Grade A or Grade B.

So, we are looking for male students who earned either an A or B grade.

### Step 2: Count the Favorable Outcomes
From the table:
- Male students who earned grade A: 8 students.
- Male students who earned grade B: 9 students.

Adding these two groups together gives the total number of favorable outcomes:
\[ 8 + 9 = 17 \]

### Step 3: Calculate the Total Number of Outcomes
The total number of students in the group is 63.

### Step 4: Calculate the Probability
The probability \( P \) that a randomly chosen student is both male and did not earn a grade C is given by the ratio of favorable outcomes to total outcomes:
\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of students}} = \frac{17}{63}
\]

### Step 5: Compute and Round to Four Decimal Places
Now, let's compute the value:
\[
P = \frac{17}{63} \approx 0.2698
\]

So, the probability that a randomly chosen student was not female and did not earn grade C is **0.2698**.

Would you like further details on any step, or have any other questions?

Here are 5 related questions:
1. How do you calculate the probability that a student is male and earned a grade C?
2. What is the probability that a student earned grade B, regardless of gender?
3. How would the probability change if one more male student earned grade A?
4. What is the probability that a student chosen at random is female and earned grade A?
5. How do you determine if two events, such as gender and grade, are independent?

**Tip:** When calculating probabilities, ensure that the total number of outcomes always reflects all possible outcomes for the scenario at hand.

Learn how to calculate the probability that a randomly chosen student is male and did not earn a grade C, based on the given gender and grade distribution. This example uses basic probability formulas and is suitable for high school students in Grades 9-12.

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