AP Stat Probability and Randomness

Given the probabilities P(A)=0.4 and P(A∪B)=0.6, what is the probability P(B) if A and B are mutually exclusive? If A and B are independent?

• 0.2, 0.4
• 0.2, 0.33
• 0.33, 0.2
• 0.6, 0.33

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 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

Which of the following are true statements?
-The histogram of a binomial distribution with p=0.5 is always symmetric no matter what n is.
-The histogram of a binomial distribution with p=0.9 is skewed to the right.
-The histogram of a binomial distribution with p=0.9 appears almost symmetric if n is very large.

• I and II
• I and III
• I, II, and III
• None of the above gives the complete set of true responses.

A computer technician notes that 40% of computers fail because of the hard drive, 25% because of the monitor, 20% because of a disk drive, and 15% because of the microprocessor. If the problem is not in the monitor, what is the probability that it is in the hard drive?

• 0.150
• 0.400
• 0.417
• 0.533

The law of large numbers states that when an experiment is performed a large number of times, the relative frequency of an event tends to be closer to the probability of the events.

• True
• False

Sixty-five percent of all divorce cases cite incompatibility as the underlying reason. If four couples file for divorce, what is the probability that exactly two will state incompatibility as the reason?

• 0.104
• 0.207
• 0.254
• 0.311

Binomial random variables are a random variable whose value is the number of success in a binomial probability distribution

• True
• False

Can the function f(x)=(x+6)/(24), for x=1, 2, and 3, be the probability distribution for some random variables?

• Yes.
• No, because probabilities cannot be negative.
• No, because probabilities cannot be greater than 1.
• Not enough information is given to answer the question.

Relative frequency is the proportion of times than an event happened divided by the total number of times the event happened.

• True
• False

Mathematically speaking, casinos and life insurance companies make a profit because of

• The central limit theorem
• Their use of well-designed, well-conducted surveys and experiments
• Their use of simulation of probability distributions
• The law of large numbers