Among the 500 first year students of college, 270 students study computer science, 345 students study mathematics, and 175 students study both computer science and mathematics. If one student is selected at random, find the probability that he did not take either of these subjects
1011
P[C.S]=270/500
P[Maths]=345/500
P[C.S ∩ Maths]=175/500
( P[C.S U Maths] )' = ?
ANS.
( P[C.S U Maths] )' = 1-P[C.S U Maths]
=1-{P[C.S] + P[Maths] - P[C.S ∩ Maths]}
=1-{270/500 + 345/500 -175/500 }
=1-{440/500}
=1-0.88
=0.12
A(-5,3)<B (-9,7)
To find the probability that a randomly selected student did not take either computer science or mathematics, we need to determine the number of students who did not take either subject and divide it by the total number of students.
First, let's calculate the number of students who took either computer science or mathematics. We can do this by adding the number of students who took computer science and mathematics and then subtracting the number of students who took both subjects (as they were counted twice).
Number of students who took computer science = 270
Number of students who took mathematics = 345
Number of students who took both computer science and mathematics = 175
Total number of students who took either computer science or mathematics = (270 + 345) - 175 = 440
Now subtract this number from the total number of students to get the number of students who did not take either subject:
Number of students who did not take either subject = total number of students - number of students who took either subject
Number of students who did not take either subject = 500 - 440 = 60
Finally, we can calculate the probability that a randomly selected student did not take either subject:
Probability = Number of students who did not take either subject / Total number of students
Probability = 60 / 500
Probability ≈ 0.12 or 12% (rounded to two decimal places)
Therefore, the probability that a randomly selected student did not take either computer science or mathematics is approximately 0.12 or 12%.