In a high-school, 135 freshmen were interviewed. Thirty-five of them took PE, 42 took BIO, 60 took ENG, 10 took PE and BIO, 15 took PE and ENG, 7 took BIO and ENG, and 5 took all three subjects.

How many students did not take ENG or BIO?

What is the probability that a randomly-chosen student from this group did not take exactly two subjects?

The number of students that did not take ENG or BIO is : 40 and the probability that a student chosen at random from the group did not take exactly two subjects is 118/135

What is a set?

A set is a collection of well-defined objects.

Each element in a set is called a member.

Analysis:

students that took PE n(PE) = 35

students that took BIO n(BIO) = 42

students that took ENG n(ENG) = 60

students that took all three subjects n(PE n BIO n ENG) = 5

students that took PE and ENG only n(PE n ENG n BIO') = 15-5 = 10

students that took PE and BIO only n(PE n BIO n ENG') = 10 - 5 = 5

students that took BIO and ENG only n( BIO n ENG n PE') = 7-5 = 2

students that took PE only = 35 -(10+5+5) = 15

students that took BIO only = 42-(10+5+2) = 25

students that took ENG only = 48 - (5+5+2) = 48

Total number of students that took either BIO, ENG or PE = 48+2+5+5+15+10+25 = 110

students that did not take the three subjects = 135 - 110 = 25

Students that did not take either ENG or BIO are students that did not take the three subjects + those that took PE only = 25 = 15 = 40

total number of people that took exactly two subjects is = 10+5+2 = 17

probability the student took exactly two subjects is 17/135

probability the student did not take exactly two subjects is 1 - 17/135 = 118/135

In conclusion, the students that did not take ENG or BIO is 40, also the probability that a student chosen at random from the group did not take exactly two subjects is 118/135

Learn more about sets: brainly.com/question/2166579

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