Probability: 1-11

For which of the following probability assignments are events E and F independent?

Answer explanation

[Image needed] An SRS of young adults were surveyed as to living at their parents' home and holding a full-time job. The mosaic plot displays the data. Which is greater, (1) the probability of not living at home given not holding a full-time job or (2) the probability of not holding a full-time job given not living at home?

• The greater of the two probabilities is (1).

• The greater of the two probabilities is (2).

• The two probabilities, (1) and (2), are equal.

• This cannot be answered without knowing the probability of not living at home and not having a full-time job.

• This cannot be answered without knowing the probabilities of not living at home, of not having a full-time job, and of not living at home and not having a full-time job.

Answer explanation

What is the proper order of size for the probabilities of the following three events?

I. A randomly selected billionaire is audited by the IRS.

II. A randomly selected taxpayer is a billionaire who is audited by the IRS.

III. A randomly selected taxpayer who is audited by the IRS is a billionaire.

• P(I) < P(II) < P(III)

• P(I) > P(II) > P(III)

• P(I) < P(III) < P(II)

• P(I) > P(III) > P(II)

• P(II) < P(I) < P(III)

• The mean is 100, and the standard deviation is 20.

• The mean is 100, and the standard deviation is 30.

• The mean is 110, and the standard deviation is 5.

• The mean is 110, and the standard deviation is 20.

• The mean is 110, and the standard deviation is 30.

A fair coin is flipped 8 times. Consider the following 3 outcomes:

I. The result in order is HHHHTTTT.

II. The result in order is HTTHHTHT.

III. The result includes 4 Hs and 4 Ts.

What is a comparison of the three probabilities?

• P(I) < P(II) < P(III)

• P(II) < P(I) < P(III)

• P(III) < P(I) < P(II)

• P(I) = P(II) < P(III)

• P(III) < P(I) = P(II)

A real estate agent, working entirely on commission, weekly makes an average of $850 with a standard deviation of $260 selling property in the city and an average of $1,340 with a standard deviation of $390 selling property in the suburbs. Assuming independence of what she sells in the two locations, what are the mean and standard deviation of her total weekly sales?

• Mean = $1,095 and standard deviation = $325

• Mean = $1,095 and standard deviation = $469

• Mean = $2,190 and standard deviation = 4325

• Mean = $2,190 and standard deviation = $469

• Mean = $2,190 and standard deviation = $650

• 1.5424

• 1.9748

• 2.379

• 3.9

• 6.1

Suppose that the probabilities that an answer can be found on Google is 0.95, on Answers.com is 0.92, and on both websites is 0.874. Are the possibilities of finding the answers on both websites independent?

• There is insufficient information to answer this question.

Suppose 80 percent of jurors come to a just decision. In a jury of six people and assuming independence, what is the probability more than half come to a just decision?

• 0.09888

• 0.34464

• 0.80000

• 0.90112

• 0.98304