Reading 3: probability concepts Flashcards
An event that includes all of the possible outcomes is said to be:
random.
exclusive.
exhaustive.
An event is said to be exhaustive if it includes all possible outcomes. (LOS 3.a)
Which of the following values cannot be the probability of an event?
0.00.
1.00.
1.25.
Probabilities may range from 0 (meaning no chance of occurrence) through 1 (which means a sure thing). (LOS 3.b)
The probability that the DJIA will increase tomorrow is 2/3. The probability of an increase in the DJIA stated as odds is:
two-to-one.
one-to-three.
two-to-three.
P(E)/[1-P(E)]= 2/3 / 1/3
two-to-one
The multiplication rule of probability determines the joint probability of two events as the product of:
two conditional probabilities.
two unconditional probabilities.
a conditional probability and an unconditional probability.
By the multiplication rule of probability, the joint probability of two events, P(AB), is the product of a conditional probability, P(A | B), and an unconditional probability, P(B). (LOS 3.d, LOS 3.e)
If events A and B are mutually exclusive, then:
P(A | B) = P(A).
P(AB) = P(A) × P(B).
P(A or B) = P(A) + P(B).
There is no intersection of events when events are mutually exclusive. P(A | B) = P(A) × P(B) is only true for independent events. Note that since A and B are mutually exclusive (cannot both happen), P(A | B) and P(AB) must both be equal to zero. (LOS 3.a, LOS 3.d)
Two mutually exclusive events:
will both occur.
cannot both occur.
may both occur.
One or the other may occur, but not both. (LOS 3.a)
At a charity ball, 800 names are put into a hat. Four of the names are identical. On a random draw, what is the probability that one of these four names will be drawn?
0.004.
0.005.
0.010.
P(name 1 or name 2 or name 3 or name 4) = 1/800 + 1/800 + 1/800 + 1/800 = 4/800 = 0.005. (LOS 3.e)
Two events are said to be independent if the occurrence of one event:
means that the second event cannot occur.
means that the second event is certain to occur.
does not affect the probability of the occurrence of the other event.
Two events are said to be independent if the occurrence of one event does not affect the probability of the occurrence of the other event. (LOS 3.f)
An analyst estimates that a share price has an 80% probability of increasing if economic growth exceeds 3%, a 40% probability of increasing if economic growth is between zero and 3%, and a 10% probability of increasing if economic growth is negative. If economic growth has a 25% probability of exceeding 3% and a 25% probability of being negative, what is the probability that the share price increases?
22.5%.
42.5%.
62.5%.
The three outcomes given for economic growth are mutually exclusive and exhaustive. The probability that economic growth is positive but less than 3% is 100% – 25% – 25% = 50%. Using the total probability rule, the probability that the share price increases is (80%)(25%) + (40%)(50%) + (10%)(25%) = 42.5%. (LOS 3.g)
P(A|B) = 40% and P(B) = 30% and P(A) = 40%. It is most likely that:
A and B are dependent.
A and B are independent.
A and B are mutually exclusive.
From the values given, P(A|B) = P(A), so A and B are independent. P(A|B) × P(B) = P(AB) = 12%, so A and B are not mutually exclusive (if they were P(AB) would equal 0). (LOS 3.g)
Given the conditional probabilities in the table below and the unconditional probabilities P(Y = 1) = 0.3 and P(Y = 2) = 0.7, what is the expected value of X?
chart in textbook:(
5.0.
5.3.
5.7.
E(X | Y = 1) = (0.2)(0) + (0.4)(5) + (0.4)(10) = 6
E(X | Y = 2) = (0.1)(0) + (0.8)(5) + (0.1)(10) = 5
E(X) = (0.3)(6) + (0.7)(5) = 5.30
(LOS 3.k)
A discrete uniform distribution (each event has an equal probability of occurrence) has the following possible outcomes for X: [1, 2, 3, 4]. The variance of this distribution is closest to:
1.00.
1.25.
2.00.
Expected value = (1/4)(1 + 2 + 3 + 4) = 2.5
Variance = (1/4)[(1 – 2.5)2 + (2 – 2.5)2 + (3 – 2.5)2 + (4 – 2.5)2] = 1.25
Note that since each observation is equally likely, each has 25% (1/4) chance of occurrence. (LOS 3.k)
The correlation of returns between Stocks A and B is 0.50. The covariance between these two securities is 0.0043, and the standard deviation of the return of Stock B is 26%. The variance of returns for Stock A is:
0.0011.
0.0331.
0.2656.
[0.0043/(.26)(.50)]^2
=0.0011
An analyst believes Davies Company has a 40% probability of earning more than $2 per share. She estimates that the probability that Davies Company’s credit rating will be upgraded is 70% if its earnings per share are greater than $2 and 20% if its earnings per share are $2 or less. Given the information that Davies Company’s credit rating has been upgraded, what is the updated probability that its earnings per share are greater than $2?
50%.
60%.
70%.
28%/ 28% + 12% = 70
Consider a universe of 10 bonds from which an investor will ultimately purchase six bonds for his portfolio. If the order in which he buys these bonds is not important, how many potential 6-bond combinations are there?
7.
210.
5,040.
10!/(10-6)!6! = 10!/4!6! = 210
