Chapter 12 Flashcards
Factorials
n!
Permutation
arrangement with no repetition and order is important
Combination
no repeat, order is not important
Probability
P=n(E)/n(S), or the number of favorable outcomes over the number of possible outcomes
Theoretical Probability
based on the assumption that all events are equally likely
Empirical Probability
based on results from an actual experiment
Calculating Empirical Probability
P(E)= number of occurrences of E/number of times the experiment was run
Odds
ratio of favorable outcomes to unfavorable outcomes
Odds in favor
a to b or a/b
Odds against
b to a or b/a
a + b = total outcomes
P(E) = a/a + b
AND
Multiply
OR
Add (and subtract)
Mutually exclusive
Two events a and b are mutually exclusive if they cannot occur at the same time
Probability of mutually exclusive events
P (a U b) = P (A) + P (B)
Addition Rule of Probability
P (a U b)= P(A) + P(B) - P(A ∩ B)
Complement
The complement of event E denoted E^C is the opposite of event E
E U E^C= S
E ∩ E^C = 0
Probability of the Complement
P(E^C) = 1 - P(E)
Expectation or Expected Value
E = S1 X P(S1) + S2 X P(S2) + S3 X P(S3)… SN X P(SN)
Sample Space
the set of all possible outcomes in an event
{1, 2, 3…}
Event
an event is one or more of the possible outcomes in an experiment
Fundamental Counting Principle
the method of determining the outcome of a multi-stage experiment
n1 X n2 X n3….
Conditional Probability
P (B|A) = P (A and B) / P (A)
The probability of B given that A has occured
Product Rule for Probabilities
P(A and B) = P(A) X P(B|A)
Probability of Successive Events
The probability of two or more events occurring in succession is the product of the conditional probabilities of each event (multiplied)
Independent Events
P(B|A) = P(B)
Product Rule for Independent Events
P(A and B)= P(A) X P(B)
