Chapter 6 problems (FROM CH 6 HANDOUT)

Which of the following statements is correct if the events A and B have nonzero probabilities? a. A and B cannot be both independent and disjoint b. A and B can be both independent and disjoint c. A and B are always independent d. A and B are always disjoint

A [?????? Disjoint is not in the textbook]

*TRUE OR FALSE* If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive

False (A and B are BOTH exhaustive and exclusive)

*TRUE OR FALSE* If either event A or event B must occur, they are called mutually exclusive.

False (Mutually exclusive only means that they cant happen at the same time)

When you multiply a first level branch with a second level branch on a probability tree you get a

Joint probability

The first set of branches of a probability tree represent

Marginal probabilities

*TRUE OR FALSE* If A and B are independent events with P(A) = .40 and P(B) = .50, then P(A and B) = .20.

True [LOOK AT CH 6 FORMULAS]

*TRUE OR FALSE* If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive

false (A and B are BOTH exhaustive and exclusive)

If the outcome of event A is not affected by event B, then events A and B are said to be

independent

Conditional probabilities are also called

likelihood probabilities

The relative frequency approach to probability uses

long term relative frequencies, often based on past data

A posterior probability value is a prior probability value that has been (#168)

modified on the basis of new information.

If either event A or event B must occur, then A and B are

mutually exclusive and collectively exhaustive events

In applying Bayes' Law, as the prior probabilities increase,

the posterior probabilities also increase

The marginal probability of A is

the probability that A occurs, regardless of whether event B occurred or not

*TRUE OR FALSE* Two or more events are said to be independent when the occurrence of one event has no effect on the probability that another will occur

true

In Bayes Law, if P(A|B) is a likelihood probability what is the posterior probability?

P(B|A)

If two events are mutually exclusive, what is the probability that both occur at the same time?

0

If two events are collectively exhaustive, what is the probability that one or the other occurs?

1 [If two events are exhaustive, that means the list covers all possible outcomes, so one of the two MUST occur]

If you roll a balanced die 50 times, you should expect an even number to appear: (a) On every other roll (b) Exactly 50 times out of 100 rolls (c) 25 times on average, over the long term (d) All of the choices are true

C [3/6 * 50 = 25]

If A and B are mutually exclusive events with P(A) = 0.75, then P(B): a. can be any value between 0 and 1. c. cannot be larger than 0.25. b. can be any value between 0 and 0.75. d. equals 0.25.

C (It would be D if it was both exclusive and exhaustive)

The second set of branches of a probability tree represent

Conditional Probabilities

If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is: a. 0.25 b. 0.40 c. 0.90 d. cannot be determined from the information given

D [If these events were independent, then we could figure out P(A and B), but its not so we dont have enough information]

*TRUE OR FALSE* If events A and B have nonzero probabilities, then they can be both independent and mutually exclusive.

False

*TRUE OR FALSE* Posterior probabilities can be calculated using the addition rule for mutually exclusive events.

False

*TRUE OR FALSE* P(A) + P(B) = 1 for any events A and B that are mutually exclusive.

False

*TRUE OR FALSE* If A and B are independent events with P(A) = 0.35 and P(B) = 0.55, then P(A|B) is 0.35/0.55 = .64

False [P(A|B) MUST equal P(A) to be an independent event]

Bayes' Law is used to compute what kind of probabilities? (#171)

Posterior probabilities

Predicting the outcome of a football game uses what approach to probability?

Subjective Judgement

*TRUE OR FALSE* If A and B are two independent events with P(A) = 0.9 and P(B|A) = 0.5, then P(A and B) = 0.45

True

*TRUE OR FALSE* We can use the joint and marginal probabilities to compute conditional probabilities, for which a formula is available.

True

*TRUE OR FALSE* Suppose the probability that a person owns both a cat and a dog is 0.10. Also suppose the probability that a person owns a cat but not a dog is 0.20. The marginal probability that someone owns a cat is 0.30

True [Draw out a bi variance table]

Which of the following is equivalent to P(A|B)? a. P(A and B) b. P(B|A) c. P(A)|P(B) d. None of these choices.

C (Probability of A given probability of B)

If two events are collectively exhaustive, what is the probability that both occur at the same time?

Cannot be determined from the information given

If two events are mutually exclusive, what is the probability that one or the other occurs?

Cannot be determined from the information given

If two events are independent, what is the probability that they both occur?

Cannot be determined from the information given [The definition of Independent events is that the probability of one event is NOT affected by the occurrence of the other event]

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the

Classical Approach

Bayes' Law allows us to [#151]

compute conditional probabilities from other forms of probability.