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.