Probability Concepts

Question 1

Empirical probability

Answer 1

• based on past data

- analyzing the frequence of an event’s occurrence in the past

Question 2

Priori probability

Answer 2

• based on reasoning / logic

Question 3

Subjective probability

Answer 3

• informed guess based on personal judgement

Question 4

Odds for an event occurring:

Answer 4

• Odds for E = P(E) / [1 - P(E)]

Question 5

Implied probability of E given “a to b”

Answer 5

• implied probability of E = a / (a + b)

Question 6

Odds against an event occurring:

Answer 6

• odds against E = [1 - P(E)] / P(E)

Question 7

Implied probability against E given “a to b”

Answer 7

• implied probability against E is = b / (a + b)

Question 8

Unconditional probability, aka…

Answer 8

the ‘marginal’ probability

Question 9

Unconditional probability def

Answer 9

• the probability of an event occurring irrespective of the occurrence of other events
• P(A)

Question 10

Conditional probability

Answer 10

• the probability of an event occurring given that another event has occurred
• P(A|B)

Question 11

Multiplication rule is used for:

Answer 11

• used for determining the joint probability of two events

- P(AB)

Question 12

Multiplication rule formula:

Answer 12

P(AB) = P(A|B) * P(B)

also

P(BA) = P(B|A) * P(A)

The probability that both A AND B will occure

Question 13

Formula for computing conditional probabilities:

Answer 13

• P(A|B) = P(AB) / P(B)

Question 14

Addition Rule for probability:

Answer 14

• used to determine the probability that at least one of the events will occur
• the probability that A OR B occurs, OR both occur

Question 15

Addition Rule probability formula

and formula if mutually exclusive

Answer 15

• P(A or B) = P(A) + P(B) - P(AB)

if mutually exclusive:
- P (A or B) = P(A) + P(B)

Question 16

Multiplication rule for independent events =

Answer 16

= P(AB) = P(A) * P(B)

Question 17

Addition rule for independent events =

Answer 17

• P(A or B) = P(A) + P(B) - P(AB)

* the addition rule does not change

Question 18

The Total Probability Rule …

Answer 18

• TPR enables us to state unconditional probabilities in terms of conditional probabilities

S= scenario
Sc = non-S

Question 19

Total Probability Rule formulas for P(A) =

Answer 19

• =P(A) = P(AS) + P(ASc)

- = P(A) = P(A|S)P(S) + P(A|Sc)P(Sc)

Question 20

Expected Value of a Random Variable is

Answer 20

• the probability-weighted average of the possible outcomes of the random variable

State of Econ. | Prob. | CF. | E(x) =
Good | .3 | $50 | =.3 50
Avg | .5 | $40 | = .540
Weak | .2 | $20 | = .2*20

E(x) = $39

Question 21

Variance of a Random Variable

Answer 21

• the probability-weighted sum of the squared differences between each possible outcome and the expected value of the random variable
• use financial caluclator

Question 22

Find the variance of a random variable on the financial calculator

State of Econ. | Prob. | CF. | E(x) =
Good | .3 | $50 | =.3 50
Avg | .5 | $40 | = .540
Weak | .2 | $20 | = .2*20

Answer 22

CF is the X value
Prob is the Y (enter as whole number)

2nd, Data
2nd, clr wrk
X01 = $50
Y01 = 30
X02 = $40
Y02 = 50
X03 = $20
Y03 = 20
2nd, Stat
2nd, Set (press until "1 - v")
down arrow, need to see N=100 (ie proability = 100)
down arrow, X = 39 (ie the expected value of the random variable)
down arrow, Sx= 10.49 (sample stdv.)
down arrow, Ox= 10.44 (population stdv)

Question 23

Total Probability rule for expected values =

Answer 23

= E(X) = E(X|S)P(S) + E(X|Sc)P(Sc)

Question 24

Need to add covariance formulas after doing practice problems

Answer 24

k

Question 25

Correlation formula =

Answer 25

= row(p) (A,B) = Cov (A,B) / O(A) * O(B)

O is pop stdv
cal O using 2nd data method

Question 26

Variance of a portfolio formula

Answer 26

= O^2(Rp) = w1^2O1^2 + w2^2O^2 + 2w1w2CovO1*O2

take STDV of answer to get the stdv of the portfolio

Question 27

Baye’s Formula

Answer 27

=P(E | I)= P(E) * (P(I | E) / P(I))

need to use the total prob rule to solve for P(I)

Question 28

Combination

Answer 28

• when the order does not matter

nCr = n! / [(n - r)! r!]

Calculator:
n, 2nd, nCr, r

Question 29

Permutation

Answer 29

• order matters
• nPr = n! / (n-r)!

Calculator
n, 2nd, nPr, r

Question 30

Labeling

Answer 30

• the number of ways that n items can be labelled with k different labels

n! / [(n1!) * (n2!) * (nk!)