Question

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
use the drop - down menus to answer the questions.
what is the probability that a randomly chosen tenth - grader is male?
what is the probability that a randomly chosen tenth - grader is malegiven that the tenth - grader prefers geometry?
are the events“male”and“geometry”independent?

Explanation:

Step1: Calculate total number of males

Total number of males = \(33 + 47=80\)
Total number of tenth - graders = \(34 + 33+40 + 47 = 154\)
Probability that a randomly chosen tenth - grader is male \(P(M)=\frac{80}{154}=\frac{40}{77}\)

Step2: Calculate probability that a student is male given they prefer geometry

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

Step3: Check for independence

Two events \(A\) and \(B\) are independent if \(P(A|B)=P(A)\)
\(P(M)=\frac{40}{77}\approx0.519\) and \(P(M|G)=\frac{47}{87}\approx0.540\)
Since \(\frac{40}{77}
eq\frac{47}{87}\), the events “male” and “geometry” are not independent

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 \(\frac{47}{87}\). The events “male” and “geometry” are not independent.