Probability Formula Review
ADVERTISEMENT
1
2Probability Formula Review
~.
Types and characteristics of probability
~-
A~ypes
of probability
A
1:,- Classical:
peA)
= N
2. Empirical:
peA)
= ~
3.
Subjective: Use empirical formula assuming past
data
of similar events is appropriate.
B. Probability characteristics
1. Range for probability:
a
~ PeA)
~ 1
2. Value of complements: P(A) = 1 - P(A)
II. Probability rules
A. Addition is used to find the sum or union of 2 events.
1.
General rule:
P(A or B) = P(A) + P(B)
-
P(A and B)
2. Special rule:
P(A or B) = P(A) + P(B) is used when events are mutually exclusive.
B. Multiplication is used to determine joint probability or the intersection of 2 events.
1. General rule: P(A and B) = P(A) x P(B I A)
2. Special rule: P(A and B) = P(A) x P(B) is used when the events are independent.
Note: For independent events, the joint probability is the product of the marginal probabilities.
C. Bayes' theorem is used to find conditional probability.
P(A) x P(SIA)
P(AIB)
=
P(A) x P(S I A) + p( A J x p( S I A J
Note: The denominator is when condition B
happens. It happens with A and with
A.
III. Countingrules
A. The counting rule of multiple events: If one event can happen M ways and a second event
can happen N ways, then the two events can happen (M)(N) ways. For 3 events, use (M)(N)(O).
B. Factorial rule for arranging all of the items of one event: N items can be arranged in N! ways.
C. Permutation rule for arranging some of the items of one event:
P
N!
(order is important: a, b, c and c, a, b are different)
N
R
=
(N - R) !
D. Combination rule for choosing some of the items of one event:
(order is not important:abc and cba are the same and are not counted twice)
N!
NCR
=
(N-R)!(R!)
IV. Discrete probability distributions
A. Probability distributions
1.
P(x) = [X8 P(x)] is calculated for each value of x.
2. Mean of a probability distribution: Il = E(x) = L[X8 P(x)]
3. Variance of a probability distribution: V(x) = [LX2
8
P(x)] - [E(x)]2
B. Binomial distributions
n is number of trials
X is number of successes
P
( x )
=
n!
P
X
q
n-x
x! (n-x)!
where
P is probability of success
I
q, the probability of failure, is 1
-
P
Il = np, 0'2 = npq and 0' =
J
npq
C. Poisson distributions
P(x)
= I1xe-11
X!
where
Il = np
Poisson approximation of the binomial requires n ~ 30 and np < 5 or nq < 5.
76
Free Quick Notes Books
has your copies of
Quick Notes Accounting, Economics, Statistics,
and Excel Statistics Lab Manual.
Free
Business Textbooks
is a library
covering many business subjects.
Business Book Mall
has material
to enhance your career.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education