**0004.** If my new study method works, I should earn a 98 on the test. If it does not work, I will get a 79. Research suggests that there is a 75% chance it works. What is the expected value of my grade?

A. |
87.5 | B. |
93.25 | C. |
95.5 | D. |
79 | E. |
98 |

**0005.**This is an event tree problem, that is, there are no choices to be made. Work out the probabilities of each of the final outcomes.

There is a 72% chance that candidate A will win the presidency over candidate B. There is a 55% chance that candidate A's party will win control of the senate and a 30% chance that his party will win control of the house.?

**0006.** I need to take a certification exam this year. The exam cost is $200. There is a prep course for the exam, but I don't know if I need it or not. It costs $300 and if one takes it, one is certain to pass the exam. If I do not take the prep course there is a 50% chance of passing and a 50% chance of failing in which case I'd have to take the prep course anyway and then retake the test (total cost = prep course + twice the exam fee). Should I take the prep course??

**0007.** Continuation of previous question. I need to take a certification exam this year. The exam cost is $200. There is a prep course for the exam, but I don't know if I need it or not. It costs $300 and if one takes it, one is certain to pass the exam. If I do not take the prep course there is a 50% chance of passing and a 50% chance of failing in which case I'd have to take the prep course anyway and then retake the test (total cost = prep course + twice the exam fee).

It turns out that there is pre-test I can take for a fee of $25. It will tell me whether I should take the prep course or not. People who fail the pretest are more likely than the average candidate to fail the actual test if they do not take the prep course. In fact, the odds drop to only a 20 per cent chance of passing the exam on first try.

Should I pay for the pre-test and what should I do if I pass it? Fail it??

**0008.** Continuation of previous question. I need to take a certification exam this year. The exam cost is $200. There is a prep course for the exam, but I don't know if I need it or not. It costs $300 and if one takes it, one is certain to pass the exam. If I do not take the prep course there is a 50% chance of passing and a 50% chance of failing in which case I'd have to take the prep course anyway and then retake the test (total cost = prep course + twice the exam fee).

It turns out that there is pre-test I can take for a fee of $25. It will tell me whether I should take the prep course or not. People who fail the pretest are more likely than the average candidate to fail the actual test if they do not take the prep course. In fact, the odds drop to only a 20 per cent chance of passing the exam on first try.

At what pre-test price would I change my decision about taking it??