5.3 Exercise 14

A software company has developed a new computer game designed to appeal to teenagers and young adults. It is felt that there is good probability it will appeal to college students, and that if it appeals to college students it will appeal to a general youth market. To check the likelihood of appeal to college students, it is decided to test first by a sales campaign at Rice and University of Texas, Austin. The following analysis of the situation is made.

1. $H =$ the event the sales to the general market will be good
2. $S =$ the event the game appeals to college students
3. $E_{1} =$ the event the sales are good at Rice
4. $E_{2} =$ the event the sales are good at UT, Austin

Since the tests are for the reception are at two separate universities and are operationally independent, it seems reasonable to assume $\left\{H , E_{1} , E_{2}\right\} ci \left|\right. S$ and $\left\{H , E_{1} , E_{2}\right\} ci \left|\right. S^{c}$. Because of its previous experience in game sales, the managers think $P \left(S\right) = 0 . 80$. Also, experience suggests

Determine the posterior odds favoring H if sales results are satisfactory at both schools.