Chapter 4-3:

The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That is, find the probability that the subject lied, given that the test yields a positive result. Did the Subject Actually Lie? Positive Test Results No (did not lie) - 19 Yes (lied) - 42 Negative Test Results No (did not lie) - 30 Yes (lied) - 10 The probability is _____.

The probability is 0.689 Add together the positive test results. 61 42/61=0.689

In a certain country, the true probability of a baby being a girl is 0.484. Among the next eight randomly selected births in the country, what is the probability that at least one of them is a boy? The probability is _____.

The probability is 0.997. 1-0.484^8=0.997

Find the probability that when a couple has six children, at least one of them is a gril. (Assume that boys and girls are equally likely.) The probability is _____ that at least one of the six children is a girl.

The probability is _63/64_ that at least one of the six children is a girl. 2^6=64 1-1/64=63/64

The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she did not have the disease. The Individual Actually Had the Disease Positive Yes - 126 No - 38 Negative Yes - 5 No - 131 The probability is approximately _____.

The probability is approximately 0.775. Add together the No column. 169 Take 131/169=0.775

A __________ probability of an event is a probability obtained with knowledge that some other event has already occurred.

conditional

The complement of "at least one" is __________.

none.

Confusion of the inverse occurs withn we incorrectly believe __________.

P(B|A)=P(A|B).

"At least one" is equivalent to __________.

"one or more"

In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts 1 through 3 below. Students Given Four Quarters Purchased Gum - 34 Kept the Money - 12 Students Given a $1 Bill Purchased Gum - 17 Kept the Money - 33 1. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. 2. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters. 3. What do the preceding results suggest? a) A student given four quarters is more likely to have kept the money. b) A student given four quarters is more likely to have kept the money than a student given a $1 bill. c) A student given four quarters is more likely to have spent the money than a student given a $1 bill. d) A student given four quarters is more likely to have spent the money.

1. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. 0.739 Add together all the student who were given Four Quarters. 46 34/46=0.739 2. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.0.261 Add together all the students who were given Four Quarters. 46 12/46=0.261 3. What do the preceding results suggest? d) A student given four quarters is more likely to have spent the money.

Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one 0. The probability is _____.

The probability is 0.344. 10^4-9^4=3439 10^4=10000 3439/10000=0.344

The conditional probability of B given A can be found by __________. a) adding P(A) and P(B) b) assuming that event B has occured, and then calculating the probability that event A will occur c) assuming that event A has occurred, and then calculating the probability that event B will occur d) multiplying P(A) times P(B)

c) assuming that event A has occurred, and then calculating the probability that event B will occur

Assume that there is a 7% rate of disk drive failure in a year. 1. If all your computer data is stored on a hard disk drive with a copy stored ona second disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? With two hard disk drives, the probability that catastrophe can be avoided is _____. 2. If copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? With three hard disk drives, the probability that catastrophe can be avoided is __________.

1. With two hard disk drives, the probability that catastrophe can be avoided is 0.9951 1-0.07^2=0.9951 2.With three hard disk drives, the probability that catastrophe can be avoided is 0.999657 1-0.07^3=0.999657

The accompanying table shows the results from a test for a certain disease. Find the probability of selecting a subject with a negative test result, given that the subject has the disease. What would be an unfavorable consequence of this error? The Individual Actually had the Disease Positive Yes - 334 No - 2 Negative Yes - 19 No - 1179 The probability is ______. What would be an unfavorable consequence of this error? a) The subject would not receive treatment and could spread the disease. b) The test would be shown to be not reliable. c) The subject would experience needless stress and additional testing. d) The test would be shown to be not effective.

The probability is 0.054. Add together the yes column. 353 19/353=0.054

Assuming boys and girls are equally likely, find the probability of a couple having a baby boy when their fifth child is born, given that the first four children were all boys. The probability is _____.

The probability is 1/2.

Let event A= subject is telling the truth and event B= polygraph test indicates that the subject is lying. Use your own words to translate the notation P(B|A) into a verbal statement. a) The probability that the polygraph indicates lying given that the subject is actually telling the truth. b) The probability that the polygraph indicates laying given that the subject is actually lying. c) The probability that the polygraph indicates truthfulness given that the subject is actually telling the truth. d) The probability that the polygraph indicates truthfulness given that the subject is actually lying.

a) The probability that the polygraph indicates lying given that the subject is actually telling the truth.