EXAMPLES 3.4.14: SOME PRACTICE EXERCISES

If a student is randomly selected, what is the probability that he/she...

1. ... had a grade of C?

Answer: 4/78 = .051

2. ...didn't have an F?

Answer: 34/78 = .436

3. ...had an A?

Answer: 0

4. Suppose that the football team plays six home games this year, including games against Georgia Tech and Miami. If Gomer's uncle randomly picks two of his six tickets to give

to Gomer, what is the probability that they will be for the Georgia Tech and Miami games?

Answer: The number of possible outcomes is C(6,2) = 15.

There are 15 possible 2-game combinations; of these, exactly one is the combination in question, so the probability is 1/15.

5. So far this basketball season, Plato has attempted 82 free throws and has made 62 of them. What is the probability that he will make a given free throw?

Answer: Based on this data, the probability that he will make a free throw is 62/82 or .756

6 - 8: A poll (1999) by the Colonial Williamsburg Foundation revealed the following (this data is authentic):

79% of Americans know that "Just Do It" is a Nike slogan.

47% know that the phrase "Life, Liberty and the Pursuit of Happiness" is found in the Declaration of Independence.

9% know that George Washington was a Revolutionary War general.

6. What is the probability that an American knows that the phrase "Life, Liberty and the Pursuit of Happiness" is found in the Declaration of Independence?

A. 47/79

B. 47/135

C. 47/88

D. 47/100

ANSWER: D (47%)

7. What is the probability that an American knows that George Washington was a Revolutionary War general?

A. .9

B. .1

C. .09

D. .01

ANSWER: C (9%)

8. What is the probability that an American does not know that "Just Do It" is a Nike slogan?

A. .79

B. .21

C. 7.9

D. 2.1

ANSWER: B (1 - .79 = .21)

9. What are the odds in favor of a randomly selected American knowing that "Just Do It" is a Nike slogan?

A. 79:100

B. 21:100

C. 79:21

D. 21:79

ANSWER: C

EXAMPLE 3.4.15

A "combination" lock has a three-number "combination" where the numbers are chosen from the set {1, 2, 3, ... , 19,20}.

What is the probability that the "combination" has no repeated numbers?

A. .00015

B. .75

C. .15

D. .855

ANSWER: D

The number of possible 3-number combinations is (20)(20)(20) = 8000.

The number of 3-number combinations having no repeated numbers is (20)(19)(18) = 6840.

6840/8000 = .855

EXAMPLE 3.4.16

Gomer is taking a 25-question multiple-choice test. He needs to get a 100% on this test in order to get a C- in the course. He knows the answers to 21 of the questions, but is clueless on the other 4 problems. If he just guesses at the other 4 problems, what is the probability that he will get a score of 100%? There are 4-choices, A, B, C and D, for each problem.

A. .25

B. .0625

C. .004

D. .625

ANSWER: C

For each of the four questions about which he is clueless, there are four possible answers. Thus, the number of ways in which he can answer those four questions is (4)(4)(4)(4) = 256. Of these 256 ways to answer the four questions, only one will be correct for all four answers.

1/236 = 0.0039. The best choice is C.