1) Subjective probability implies that we can measure the relative frequency of the values of the random variable.
2) The use of “expert opinion” is one way to approximate subjective probability values.
3) Mutually exclusive events exist if only one of the events can occur on any one trial.
4) Stating that two events are statistically independent means that the probability of one event occurring is independent of the probability of the other event having occurred.
5) Saying that a set of events is collectively exhaustive implies that one of the events must occur.
6) Saying that a set of events is mutually exclusive and collectively exhaustive implies that one and only one of the events can occur on any trial.
7) A posterior probability is a revised probability.
8) Bayes’ theorem enables us to calculate the probability that one event takes place knowing that a second event has or has not taken place.
9) A probability density function is a mathematical way of describing Bayes’ theorem.
10) The probability, P, of any event or state of nature occurring is greater than or equal to 0 and less than or equal to 1.
11) A probability is a numerical statement about the chance that an event will occur.
12) If two events are mutually exclusive, the probability of both events occurring is simply the sum of the individual probabilities.
13) Given two statistically dependent events (A,B), the conditional probability of P(A|B) = P(B)/P(AB).
14) Given two statistically independent events (A,B), the joint probability of P(AB) = P(A) + P(B).
15) Given three statistically independent events (A,B,C), the joint probability of P(ABC) = P(A) × P(B) × P(C).
16) Given two statistically independent events (A,B), the conditional probability P(A|B) = P(A).
17) Suppose that you enter a drawing by obtaining one of 20 tickets that have been distributed. By using the classical method, you can determine that the probability of your winning the drawing is 0.05.
18) Assume that you have a box containing five balls: two red and three white. You draw a ball two times, each time replacing the ball just drawn before drawing the next. The probability of drawing only one white ball is 0.20.
19) If we roll a single die twice, the probability that the sum of the dots showing on the two rolls equals four (4), is 1/6.
20) For two events A and Bthat are not mutually exclusive, the probability that either Aor B will occur is P(A) × P(B) – P(A and B).
21) If we flip a coin three times, the probability of getting three heads is 0.125.
22) Consider a standard 52-card deck of cards. The probability of drawing either a seven or a black card is 7/13.
23) Although one revision of prior probabilities can provide useful posterior probability estimates, additional information can be gained from performing the experiment a second time.
24) If a bucket has three black balls and seven green balls, and we draw balls without replacement, the probability of drawing a green ball is independent of the number of balls previously drawn.
25) Assume that you have an urn containing 10 balls of the following description:
4 are white (W) and lettered (L)
2 are white (W) and numbered (N)
3 are yellow (Y) and lettered (L)
1 is yellow (Y) and numbered (N)
If you draw a numbered ball (N), the probability that this ball is white (W) is 0.667.
26) Assume that you have an urn containing 10 balls of the following description:
4 are white (W) and lettered (L)
2 are white (W) and numbered (N)
3 are yellow (Y) and lettered (L)
1 is yellow (Y) and numbered (N)
If you draw a numbered ball (N), the probability that this ball is white (W) is 0.60.
27) Assume that you have an urn containing 10 balls of the following description:
4 are white (W) and lettered (L)
2 are white (W) and numbered (N)
3 are yellow (Y) and lettered (L)
1 is yellow (Y) and numbered (N)
If you draw a lettered ball (L), the probability that this ball is white (W) is 0.571.
28) The joint probability of two or more independent events occurring is the sum of their marginal or simple probabilities.
29) The number of bad checks written at a local store is an example of a discrete random variable.
30) Given the following distribution:
Outcome
Value of
Random Variable
Probability
A
1
.4
B
2
.3
C
3
.2
D
4
.1
The expected value is 3.