AP Statistics / Mr. Hansen
Extra Review Problems for 12/7/00 Test

Name: _________________________

1.

Let A = the event of getting an even outcome on a die roll, B = the event of getting two heads when two fair coins are tossed, and C = the event of getting a 5 on a die roll.

(a)

The probability of getting two heads, given that the die roll is even = _______ . Are A and B independent? ____ Why or why not? ______

(b)

The probability of getting an even die roll and two heads = _______ . Are A and B disjoint? _____ Why or why not? _______
Are A and B mutually exclusive? _____ Why or why not? _______

(c)

The probability of getting an even die roll or two heads = _______ .

(d)

The probability of getting an even die roll or a 5 = _______ . Are A and C disjoint? _____ Why or why not? _______

(e)

Are A and C independent? _____ Why or why not? ________

(f)

Compute the probability of getting an even die roll and two heads, or of getting a die roll that is not a 5.

(g)

Compute the probability of getting a 5, given that the roll was not even or the coins both came up heads.

2.

The fiendish Mr. Han Sen, a lecturer in statistics at Hong Kong University, was fond of conducting quizzes to discourage students from skipping (i.e., ditching) required assemblies. For examples, after a lecture on ethics, Han Sen would often ask the students to summarize the key points of the lecture. Needless to say, students hated these quizzes and conspired to foil the evil Han Sen’s tactics.

An omniscient observer concluded that for an upcoming lecture by Chris Matthews and John B. Anderson, 30% of the students would skip the assembly, 64% would attend, and 6% would have legitimate excused absences of one sort or another. Of those who skipped the lecture, 70% would be found out by Han Sen’s quiz and would be subjected to a punishment of unspeakable cruelty. However, because of sheer luck, willpower, and/or their indomitable human spirit, about 30% of the skippers would be able to pass the quiz. Of those who attended the lecture, 99% would be able to pass the quiz, but 1% would be falsely accused by Han Sen of having an unexcused absence. Students with excused absences would be listed on an official memorandum and thus would escape harassment, but all other students would be subjected to the quiz.

(a)

You may assume for this problem that HKU has a huge enrollment (many thousands of students). Make a tree diagram. Then find or compute each of the following:

(b)

the sensitivity of the quiz

(c)

the specificity of the quiz

(d)

the probability that a student is accused by Han Sen of skipping the assembly

(e)

the probability that a student is among those who pass the quiz

(f)

the probability that a student is falsely accused, given that s/he actually attended the assembly

(g)

the probability that a student passed the quiz or avoided taking the quiz altogether

(h)

the probability that a student skipped the assembly, given that the student did not have an excused absence

(i)

the probability that a student actually skipped the assembly, given that s/he failed the quiz