Questions: Giving a test to a group of students, the grades and gender are summarized below A B C Total --------------- Male 15 16 7 38 Female 5 2 9 16 Total 20 18 16 54 Answer the following using fractions or decimals rounded to three places. a. Find the probability that the student received an A in the class. b. Find the probability that the student is a female. c. Find the probability that the student was a male and received an A in the class. d. Find the probability that the student received an A in the class, given they are female. e. Find the probability that the student is a female given they received an A in the class. f. Find the probability that the student is a female and received an A in the class. g. Find the probability that the student received an A given they are female.

Solution Steps

To solve the given problem, we need to calculate probabilities based on the provided data. Here are the steps for each part:

a. To find the probability that a student received an A, we divide the number of students who received an A by the total number of students. b. To find the probability that a student is female, we divide the number of female students by the total number of students. c. To find the probability that a student is male and received an A, we divide the number of male students who received an A by the total number of students.

To find the probability that a student received an A, we use the formula:

\[ P(A) = \frac{\text{Number of students with A}}{\text{Total number of students}} = \frac{20}{54} \approx 0.370 \]

To find the probability that a student is female, we apply the formula:

\[ P(\text{Female}) = \frac{\text{Number of female students}}{\text{Total number of students}} = \frac{16}{54} \approx 0.296 \]

To find the probability that a student is male and received an A, we use the formula:

\[ P(\text{Male and A}) = \frac{\text{Number of male students with A}}{\text{Total number of students}} = \frac{15}{54} \approx 0.278 \]

Final Answer