Question

determining if events are independent
the 154 tenth - graders at wilson high school were polled on whether they enjoyed their algebra or geometry course more. the results are shown.

• algebra: 34 female, 33 male
• geometry: 40 female, 47 male

what is the probability that a randomly chosen tenth - grader is male?
what is the probability that a randomly chosen tenth - grader is male given that the tenth - grader prefers geometry?

Explanation:

Step1: Calculate total number of males

Total number of males = \(33 + 47=80\)
Total number of students \(=34 + 33+40 + 47 = 154\)
Probability that a student is male \(P(M)=\frac{\text{Number of males}}{\text{Total number of students}}\)
\(P(M)=\frac{80}{154}=\frac{40}{77}\)

Step2: Calculate number of males who prefer geometry

Number of males who prefer geometry \(= 47\)
Number of students who prefer geometry \(=40 + 47=87\)
Probability that a student is male given geometry preference \(P(M|G)=\frac{\text{Number of males in geometry}}{\text{Number of students in geometry}}\)
\(P(M|G)=\frac{47}{87}\)

Answer:

The probability that a randomly - chosen tenth - grader is male is \(\frac{40}{77}\).
The probability that a randomly - chosen tenth - grader is male given that the tenth - grader prefers geometry is \(\frac{47}{87}\).