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 below. 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 male given that the tenth - grader prefers geometry? are the events \male\ and \geometry\ independent?

Explanation:

Step1: Calculate total number of male students

Total male students = 33 + 47 = 80
Total students = 34+33 + 40+47 = 154

Step2: Calculate probability of a student being male

Probability (male) = $\frac{\text{Number of male students}}{\text{Total number of students}}=\frac{80}{154}=\frac{40}{77}$

Step3: Calculate number of students who prefer geometry

Number of students who prefer geometry = 40 + 47 = 87

Step4: Calculate probability of a student being male given they prefer geometry

Probability (male|geometry) = $\frac{\text{Number of male students who prefer geometry}}{\text{Number of students who prefer geometry}}=\frac{47}{87}$

Step5: Check for independence

Two events A (being male) and B (preferring geometry) are independent if P(A)×P(B)=P(A and B)
P(A) = $\frac{80}{154}$, P(B)=$\frac{87}{154}$, P(A and B)=$\frac{47}{154}$
P(A)×P(B)=$\frac{80}{154}\times\frac{87}{154}=\frac{6960}{23716}
eq\frac{47}{154}$
So the events are not independent.

Answer:

What is the probability that a randomly - chosen tenth - grader is male? $\frac{40}{77}$
What is the probability that a randomly - chosen tenth - grader is male given that the tenth - grader prefers geometry? $\frac{47}{87}$
Are the events "male" and "geometry" independent? No