AP Statistics / Mr. Hansen	Name: _______________________________________
12/13/2006	Mr. Hansen’s use only (bonus point for spare batteries): _______

Quest on Probability (70 pts.)

• Calculator is OK throughout.
• Point values are as follows: 20 pts. (4 + 10 + 6) for #2, 4 pts. for #8, 4 pts. for #11, and 6 pts. each for the others. Since there is no problem #5, students who mark the typo get ½ point bonus.
• If a blank is provided, give the short answer that fits best.
• If a gap is provided, provide adequate justification/explanation, and circle your answer.

1.	We will draw 2 cards, without replacement, from a well-shuffled deck. Let A be the event that a 7 is drawn on the first draw, and let B be the event that an 8 is drawn on the second draw. Are A and B mutually exclusive? (Write “yes” or “no.”) _______ Are A and B independent? _______ Compute P(A Ç B), correct to 6 decimal places: _______
2.	In yesterday’s Physics Egg Drop Competition, conducted by Dr. Morse, the probability of a completely unscathed egg was 0.6, and the probability of an egg being unscathed or only cracked was 0.76. All other eggs were smashed. Let U be the universe of all eggs that were dropped yesterday. Draw a Venn diagram to illustrate the universe, as well as the relationship among events G (good drop), O (OK drop with no more than a crack), and S (smashed). Use the blank region below. Also state the following to 3 decimal places of accuracy: P(O Ç ~G) = _______ P(G | O) = _______ P(O | G) = _______ P(S) = _______ P(S È G) = _______ Explain carefully why S and G are mutually exclusive but not independent. Label the probabilities that you use in your proof.
3.	Two fair dice are rolled. Compute the probability of an even sum, given that neither die is a 1. Show your work (no credit without work).
4.	I feel lucky, and I think I can roll snake eyes (double 1) on my next roll of the dice. You offer to bet me with payout odds of 35:1. Is this a fair game? _______ Compute the expected value of the game for each dollar that I wager. (Work is needed for credit.)
6.	Write a simulation methodology to address the following question. Do not actually solve the problem. An airplane has 100 passenger seats. However, no obese person can board if 2 or more obese people are already seated on that side of the fuselage. The fuselage has 2 sides (left and right, with 50 seats on each side). All 100 seats are reserved and assigned to passengers, 10% of whom are obese. We wish to know the probability that the third obese passenger to attempt to board will be denied boarding.
7.	Again, if 10% of airline passengers are obese, compute the probability that an SRS of 9 (from a large pool) will include at least one obese person. Then explain why your answer would be different (1 short sentence) if the pool consisted of only the 100 passengers in #6.
8.	State p and q in #7. (Write equations.) _______ = _______ , _______ = _______
9.	A screening test for yawnitis is 99% sensitive (i.e., P(pos. | infected) = 0.99) and 97% selective (i.e., P(neg. | not infected) = 0.97). Compute the PPV of the test if yawnitis affects 2% of all students.
10.	PPV stands for ____________  ____________  ____________ and means ____________________________________________________________ .
11.	A reinsurance company is _________________________________________ .