There are 1000 juniors in a college Among the 1000 juniors 2

There are 1000 juniors in a college. Among the 1000 juniors, 200 students are in the STAT roster, and 100 students are in the PSYC roster. There are 80 students taking both courses.

a) What is the probability that a randomly selected junior is taking at least one of these two courses?
b) What is the probability that a randomly selected junior is taking PSYC, given that he/she is taking STAT?

Solution

given total students N = 1000.

No of students taking STAT roster = N(A) = 200.

No of students taking PSYC course = N(B) = 100.

Studentsw taking both courses = N(A & B) = 80.

No of students taking atleast one course = N(A U B) = N(A) + N(B) - N(A &B) = 200+100-80 = 220.

Probablity that a randomly selected student has taken atleast one course = N(A U B) / N = 220/1000 = 0.220.

B.

Now given that a randomly selected sudent has taken PSYC course, then what is probablity he takes STAT.

The probability can be found by calculating the ratio of intersection of people taking two courses and people taking PSYC only which is given as

N (A & B)/N(B) = 80/100 = 0.8.

So probability that a randomly selected student who is taking PSYC course has a probability of 0.8 of taking STAT course also