APS- Unit 4B: Probability

A television game show had three payoffs with the probabilities shown in the table. What are the mean and standard deviation for the payoff variable?

• μ_x = 3667; σ_x = 4497

• μ_x = 3667; σ_x = 5508

• μ_x = 1300; σ_x = 2934

• μ_x = 1300; σ_x = 8802

• None of the above answers are correct.

An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least two of the three items are in perfect condition. If in reality 90% of the whole lots are perfect, what is the probability that the lot will be accepted?

• 0.667

• 0.729

• 0.810

• 0.900

• 0.972

Which of the following are true statements?

I. The histogram of a binomial distribution with p = 0.5 is always symmetric no matter what n, the number of trials.

II. The histogram of a binomial distribution with p = 0.9 is skewed to the right.

III. The histogram of a binomial distribution with p = 0.9 is almost symmetric if n is very large.

• I and II

• I and III

• II and III

• I, II, and III

• None of the above gives the complete set of true responses.

Five hundred people used a home test for HIV, and then underwent more conclusive hospital testing. The accuracy of the home test was evidenced in the table shown. Find the probability of testing negative given that the person does not have HIV.

• 0.583

• 0.870

• 0.950

• 0.946

• 0.125

Five hundred people used a home test for HIV, and then underwent more conclusive hospital testing. The accuracy of the home test was evidenced in the table shown. What is the probability that a person has HIV and tests positive?

• 0.07

• 0.130

• 0.538

• 0.583

• 0.875

In a 1974 "Dear Abby" letter a woman lamented that she had just given birth to her eighth child and all were girls! Her doctor had assured her that the chance of the eighth child being a girl was only 1 in 100.

a) What was the real probability that the eighth child would be a girl?

b) Before the birth of the first child, what was the probability that the woman would give birth to eight girls in a row?

• 0.5; 0.0039

• 0.0039; 0.0039

• 0.5; 0.01

• 0.5; 0.5

• 0.0039; 0.4

If P(A) = 0.2 and P(B) = 0.1, what is P(A U B) if A and B are independent?

• 0.02

• 0.28

• 0.30

• 0.32

• There is insufficient information to answer this question.

You have the choice of three investments, the first of which gives you a 10% chance of making $1 million, otherwise you lose $25,000; the second of which gives you a 50% chance of making $500,000, otherwise you lost $345,000; and the third of which gives you an 80% chance of making $50,000, otherwise you make only $1,000. Assuming you will go bankrupt if you don't show a profit, which option should you choose for the best chance of avoiding bankruptcy?

• First option

• Second option

• Third option

• Either the first or the second option

• All of the options give an equal chance of avoiding bankruptcy.

Suppose you toss a coin ten times and it comes up heads every time. Which of the following is a true statement?

• By the law of large numbers, the next toss is more likely to be tails than another heads.

• By the properties of conditional probability, the next toss is more likely to be heads given that ten tosses in a row have been heads.

• Coins actually do have memories, and thus what comes up on the next toss is influenced by the past tosses.

• The law of large numbers tells how many tosses will be necessary before the percentages of heads and tails are in balance again.

• The probability that the next toss will again be heads is 0.50.

Suppose that 60% of students who take the AP Statistics exam score 4 or 5, 25% score 3, and the rest score 1 or 2. Suppose further that 95% of those scoring 4 or 5 receive college credit, 50% of those scoring 3 receive such credit, and 4% of those scoring a 1 or 2 receive credit. If a student who is chosen at random from among those taking the exam receives college credit, what is the probability that she received a 3 on the exam?

• 0.125

• 0.178

• 0.701

• 0.813

• 0.822