Question

More than three-quarters of the nation’s colleges and universities now offer online classes, and about 23% of college graduates have taken a course online. 39% of those who have taken a course online believe that online courses provide the same educational value as one taken in person, a view shared by only 27% of those who have not taken an online course. At a coffee shop you overhear a recent college graduate discussing that she doesn’t believe that online courses provide the same educational value as one taken in person. What’s the probability that she has taken an online course before?

Answer 1

0.1997 or 19.97%

Explanation:

Have taken course online (H) = 23%

Have NOT taken course online (N) = 77%

Have taken course online and don't believe they provide same value (H&D) = 61%

Have NOT taken course online and don't believe they provide same value (N&D) = 73%

The probability that a student has taken a course online given that she does not believe that online courses provide the same educational value as one taken in person is;

`P(H|D)=(P(H)*P(H\&D))/(P(H)*P(H\&D)+P(N)*P(N\&D))\\P(H|D)=(0.23*0.61)/(0.23*0.61+0.77*0.73)\\P(H|D)=0.1997`

There is a 0.1997 or 19.97% chance that she has taken an online course before.