Answer to Question #102451 in Statistics and Probability for Jasurbek

Question

A publisher sends advertising materials for an accounting text to 80% of all professors teaching the appropriate accounting course. Thirty percent of the professors who received this material adopted the book, as did 10% of the professors who did not receive the material. What is the probability that a professor who adopts the book has received the advertising material?

Answer 1

The probability of a professor receiving a material and adopting = p(receiving material) and p( adopting the material)

=0.8*0.3

=0.24

The probability of a professor adopting the material= p(professor receiving the material and adopting) or p(professor not receiving the material and adopting)

=(0.8*0.3)+(0.2*0.1)

=0.26

The probability that a professor received the material given that  he/she adopted it= p(receiving a material  and adopting)/p(adopting the material)

=0.24/0.26

Answer

=0.9231