Question

15. Of the 360 students in the freshman class, 216 are on the honor roll and 180 play a school sport.

Of those that play a school sport, 112 are not on the honor roll. Complete the Venn diagram below to represent this situation.

16. Using the Venn diagram in question 15, if one of the students is chosen at random find: (school sport | honor roll)

Answer 1

Explanation:

15: bottom left = 360 = full freshman class

180 play a sport -- of those, 112 are NOT on the honor roll, meaning that 112 are only in a school sport. thus,

middle right = 112

180 - 112 = students that play a sport that are not not on the honor roll = students that play a sport and are on the honor roll = 68

middle center = 68

216 - 68 = students that are on the honor roll and are not in both honor roll and a sport = students that are on the honor roll and not in a sport = 148

middle left = 148

16. P(school sport | honor roll) = probability a student is on a school sport GIVEN that they are on the honor roll = P(A and B)/P(B) = 68/148 = 45.9%