determining if events are independent\nthe 154 tenth - graders at wilson high school were polled on whether…
determining if events are independent\nthe 154 tenth - graders at wilson high school were polled on whether they enjoyed their algebra or geometry course more. the results are shown below.\nalgebra: 34 female, 33 male\ngeometry: 40 female, 47 male\nuse the drop - down menus to answer the questions.\nwhat is the probability that a randomly chosen tenth - grader is male?\nwhat is the probability that a randomly chosen tenth - grader is male given that the tenth - grader prefers geometry?\nare the events \male\ and \geometry\ independent?
Answer
Explanation:
Step1: Calculate total number of males
Total males = 33 + 47 = 80 Total students = 154 Probability male = $\frac{80}{154}=\frac{40}{77}$
Step2: Calculate number of students who prefer geometry
Total students who prefer geometry = 40 + 47 = 87 Number of males who prefer geometry = 47 Probability male given prefers geometry = $\frac{47}{87}$
Step3: Check for independence
Two events A and B are independent if $P(A\cap B)=P(A)\times P(B)$. Let A be the event of being male and B be the event of preferring geometry. $P(A)=\frac{80}{154}$, $P(B)=\frac{87}{154}$, $P(A\cap B)=\frac{47}{154}$ $P(A)\times P(B)=\frac{80}{154}\times\frac{87}{154}=\frac{6960}{23716}\neq\frac{47}{154}$ 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