5.3 Exercise 12

Martha is wondering if she will get a five percent annual raise at the end of the fiscal year. She understands this is more likely if the company's net profits increase by ten percent or more. These will be influenced by company sales volume. Let

1. $H =$ the event she will get the raise
2. $S =$ the event company profits increase by ten percent or more
3. $E =$ the event sales volume is up by fifteen percent or more

Since the prospect of a raise depends upon profits, not directly on sales, she supposes $\left\{H , E\right\} ci \left|\right. S$ and $\left\{H , E\right\} ci \left|\right. S^{c}$. She thinks the prior odds favoring suitable profit increase is about three to one. Also, it seems reasonable to suppose

End of the year records show that sales increased by eighteen percent. What is the probability Martha will get her raise?