Questions: Giving a test to a group of students, the table below summarizes the grade earned by gender. A B C Total ---------------------- Male 20 16 2 38 Female18 4 6 28 Total 38 20 8 66 If one student is chosen at random, find the probability that the student is male given the student earned grade B. Round your answer to four decimal places.

Solution Steps

We need to find the probability that a randomly selected student is male given that the student earned a grade of B. This can be expressed mathematically as:

\[ P(\text{Male} | B) = \frac{P(\text{Male and } B)}{P(B)} \]

The probability that a student is both male and earned a grade of B is calculated as follows:

\[ P(\text{Male and } B) = \frac{\text{Number of males who got B}}{\text{Total number of students}} = \frac{16}{66} \]

The probability that a student earned a grade of B is given by:

\[ P(B) = \frac{\text{Total number of students who got B}}{\text{Total number of students}} = \frac{20}{66} \]

Now we can substitute the values into the formula for conditional probability:

\[ P(\text{Male} | B) = \frac{P(\text{Male and } B)}{P(B)} = \frac{\frac{16}{66}}{\frac{20}{66}} = \frac{16}{20} = 0.8 \]

Final Answer