Spring 2004 - Math For Life



Section 1: Multiple choice

1. Events A and B defined by the given Venn diagram are

(A) independent and disjoint

(B) dependent and disjoint

(C) independent and not disjoint

(D) dependent and not disjoint

(E) cannot be determined

2. If performance on AP Stat tests are independent and the probability of passing an AP Stat test is 0.2, then the probability of passing three AP Stat tests is

(A) 0

(B) 0.008

(C) 0.04

(D) 0.2

(E) 0.6

3. If [pic] ,[pic], and [pic], then find [pic].

(A) 0.11

(B) 0.23

(C) 0.48

(D) 0.52

(E) 0.77

4. If two fair dice are rolled, what is the probability of getting a sum greater than 4?

(A) 0.167

(B) 0.333

(C) 0.500

D) 0.667

E) 0.833

5. How many possible 5-character code words are possible if the first two characters are letters and the last three characters are numbers (and no character may be repeated)?

(A) 78

(B) 82

(C) 468,000

(D) 676,000

E) the number is too large for my calculator

6. In a certain game, a fair die is rolled and a player gains 20 points if the die shows a “6.” If the die does not show a “6,” the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?

(A) a gain of about 1,700 points

(B) a gain of about 583 points

(C) a gain of about 83 points

(D) a loss of about 250 points

(E) a loss of about 300 points

Section 2: Free-response questions

7. In April 2003, Science magazine reported on a new computer-based test for ovarian cancer, “clinical proteomics,” that examines a blood sample for the presence of certain patterns of proteins. Ovarian cancer, though dangerous, is very rare, afflicting only 1 of every 5000 women. The test is highly sensitive, able to correctly detect the presence of ovarian cancer in 99.97% of women who have the disease. However, it is unlikely to be used as a screening test in the general population because the test gave false positives 5% of the time. Why are false positives such a big problem? Draw a tree diagram and determine the probability that a woman who tests positive using this method actually has ovarian cancer.

8. If [pic]and [pic], find [pic] if

a) A and B are independent

b) A and B are disjoint

9. In a recent survey of 100 10-year olds, the following information was obtained:

53 liked McDonalds 12 liked both McDonalds and Burger King

24 liked Burger King 23 liked both McDonalds and Wendy’s

42 liked Wendy’s 4 liked only Burger King

6 liked all three

a) Draw a Venn diagram illustrating this information.

b) How many 10-year olds don’t like any of these three?

c) What percentage of these 10-year olds like Burger King and Wendy’s?

d) If one of these 10-year olds likes Wendy’s, what is the probability that he likes Burger King?

10. A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 40% of the cameras sold have been the basic model. Of those buying the basic model, 30% purchase an extended warranty; whereas, 50% of all purchasers of the deluxe model buy an extended warranty. Draw a tree diagram of this situation showing the probabilities of all possible events.

If you learn that a randomly selected purchaser bought an extended warranty, what is the probability that he or she has a basic model?

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B

S

A

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