More than three-quarters of the nation's colleges and universities now offer online classes, and about 23%...

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? (Round to four decimal places if necessary.)

Solutions

Expert Solution

P(have taken a course online) = 0.23

P(believe that online courses provide the same educational value | have taken a course online) = 0.39

P(believe that online courses provide the same educational value | haven't taken a course online) = 0.27

P(believe that online courses provide the same educational value) = P(believe that online courses provide the same educational value | have taken a course online) * P(have taken a course online) + P(believe that online courses provide the same educational value | haven't taken a course online) * P(haven't taken a course online)

= 0.39 * 0.23 + 0.27 * (1 - 0.23)

= 0.2976

P(doesn't believe that online courses provide the same educational value) = 1 - P(believe that online courses provide the same educational value) = 1 - 0.2976 = 0.7024

P(doesn't believe that online courses provide the same educational value | have taken a course online) = 1 - P(believe that online courses provide the same educational value | have taken a course online)

= 1 - 0.39

= 0.61

P(has taken an onlince course | doesn't believe that online courses provide the same educational value) = P(doesn't believe that online courses provide the same educational value | have taken a course online) * P(have taken a course online) / P(doesn't believe that online courses provide the same educational value)

= 0.61 * 0.23 / 0.7024

= 0.1997

orchestra answered 1 year ago

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