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.