Question

1. At Harvard University, 53% of the students are female, 60% of the students participate in an extracurricular activity, and 37% of the students drive to school. Further, 33% of the students are females who participate in an extracurricular activity, 15% are females who are drivers, and 11% of students participate in extracurricular activities and drive to school. Finally, 6% of the students are females who participate in extracurricular activities and drive to school. Pick a student at random from this university, what's the probability that the chosenstudent is a male who does not participate in extracurricular activities and does not drive toschool? (You must make a Venn Diagram, with three circles, to get full credit for this question).

Answer 1

1) We have to find the probability of randomly selecting a student that is male, who does not participate in extracurricular activities and drive to school.

We know that 53% of the students are female. Then, 100-53 = 47% of the students are male.

We can try to draw a Venn's diagram to classify the groups with the information we have:

As 60% of the students participate in extracurricular activities and 33% of the students are females that participate in extracurricular activities, then 60-33 = 27% of the students are males that participate in extracurriclar activites.

37% of the students drive to school and 15% are female students that drive to work. This tell us that 37-15 = 22% of the students are males that drive to work.

11% of the students participate in extracurricular activities and are drivers. 6% of the students are females that participate in extracurricular activities and are drivers. Then, 11-6 = 5% of the students are males that partipate in extracurricular activities and are drivers.

We can now draw a Venn's diagram for male students (for a base of 47 male students) as:

We now can estimate the probabiltiy of randomly selecting a male student that does not participate in extracurricular activities and drive to school. This correspond to the group shaded in green: male drivers that don't participate in extracurricular activities.

This group represents 17 students out of 100, so the probability of randomly selecting a male student that does not participate in extracurricular activities and drive to school is 17%.

Answer: 17%