Questions: Giving a test to a group of students, the grades and gender are summarized below A B C Total --------------- Male 9 3 5 17 Female 15 7 13 35 Total 24 10 18 52 If one student is chosen at random, A. Find the probability that the student was female: B. Find the probability that the student was female AND got a "C": C. Find the probability that the student was female OR got a "C": D. If one student is chosen at random, find the probability that the student was female GIVEN they got a 'C':

Solution Steps

To find the probability that a randomly chosen student is female, we use the formula:

\[ P(\text{Female}) = \frac{\text{Number of Female Students}}{\text{Total Number of Students}} = \frac{35}{52} \approx 0.6731 \]

Thus, the probability that the student was female is \( \boxed{0.6731} \).

Next, we calculate the probability that a randomly chosen student is both female and received a grade of "C":

\[ P(\text{Female AND C}) = \frac{\text{Number of Female Students who got C}}{\text{Total Number of Students}} = \frac{13}{52} = 0.2500 \]

Therefore, the probability that the student was female AND got a "C" is \( \boxed{0.2500} \).

To find the probability that a randomly chosen student is either female or received a grade of "C", we apply the formula for the union of two events:

\[ P(\text{Female OR C}) = P(\text{Female}) + P(\text{C}) - P(\text{Female AND C}) \]

Where:

• \( P(\text{C}) = \frac{\text{Total Students who got C}}{\text{Total Number of Students}} = \frac{18}{52} \approx 0.3462 \)

Substituting the values:

\[ P(\text{Female OR C}) = 0.6731 + 0.3462 - 0.2500 \approx 0.7692 \]

Thus, the probability that the student was female OR got a "C" is \( \boxed{0.7692} \).

Final Answer