Question

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

Answer 1

`(118)/(135)`

Explanation:

Total Number of Students =135

Number who took all three subjects=5

Number who took PE and BIO=10

Number who took PE and ENG=15

Number who took BIO and ENG=7

Therefore:

• Number who took PE and BIO only=10-5=5
• Number who took PE and ENG only=15-5=10
• Number who took BIO and ENG only =7 -5=2

Total Number of students who took exactly two subjects=5+10+2=17

Therefore:

Number of students who did not take exactly two subjects=135-17=118

The probability that a randomly-chosen student from this group did not take exactly two subjects

`=\frac{\text{Number of students who did not take exactly two subjects}}{\text{Total Number of students }} \\=(118)/(135)`