Chapter 6 probability
S
AUAc =
P(AUB) = P(A) + P(B) - P(AnB)
Addition law
P(A) + P(B) - P(AUB)
Additive: P(AnB) =
Mutually exclusive, collectively exhaustive
An event and its compliment are ______ and ______
random (stochastic) experiment
Another word for statistical experiments. Reflects influence that probability has on it and that even if exactly replicated, a different outcome can occur.
S, mutually exclusive, collectively exhaustive
Because AuA^c = ______ it is ______(words) and _____(words)
{} (empty set), mutually exclusive
Because P(AnA^c) = P(_____), it = ______
P(A), P(A^c), P(S), 1
Because P(AuA^c) = ___ + ___ = ______ = ______
1
By definition, 0! =
C = P/r!
Combination and permutation's relationship
P(A|B) = P(AnB)/P(B), P(B) != 0
Conditional Probablility formula. Use != for not equal.
0
Conditional probability for mutually exclusive events is
0
Conditional probablility for complimentary events is P(A|Complementary) =
Permutation
Counting rule where every instance is counted (order matters)
combination
Counting rule where order does not matter.
1/n
Formula for classical approach to assigning probability to experimental outcomes (N= number of outcomes).
0
If A and B are mutually exclusive, P(AnB) =
P(AUB) = P(A) + P(B)
If A and B are mutually exclusive, the additive rule becomes
True
In conditional probability, the only way that we can observe event A is for the event (AnB) to occur (True/False)
Groups, the actual things
In permutations and combinations, N = , and R =
Probability
In statistical experiments, ______ determines outcome
P(AnB)
In the addition law we subtract ______ to avoid over counting the intersection points already included in P(A) and P(B)
Classical, Relative Frequency, Subjective
3 approaches to assigning probability to experimental outcomes
Mn, combination, permutation
3 counting rules
1. Define experiment, 2. List sample points, 3. Assign Probabilities to sample points 4. Determine collection of sample points contained in event of interest 5. Sum sample point probabilities
5 steps for calculating probability
Sample point/elementary event
Denoted by O1, O2, O3,....
P(AnB) = P(A|B) * P(B) = P(B|A) * P(A) = P(BnA), P(B) != 0, P(A) != 0
Multiplication law formula. Use != for not equal
Relative frequency
No matter what method we use to assign probability m, we interpret using ______
1
P(AUAc) = P(A) + P(Ac) = P(S)=
P({})=0
P(AnAc) =
P(B|A), denominators are different
P(A|B) != , because
P(AnB)/P(A), P(A) != 0
P(B|A) =
1
P(S) =
Number of wanted outcomes/ number of possible outcomes
Probability =
Depends
Sample space (depends/ does not depend) on what is being measured
exhaustive, mutually exclusive
Sample space must be (2 properties)
Sample spaxe
Set of all possible sample points. Denoted by S
Sum
The probability of an event is the _____ of the probabilities of the simple events that constitute the event
Complementary events
Two outcomes of an event that are the only two possible outcomes. Like flipping a heads or tales, no other possible options.
Conditional Probability
Used to determine how two events are related. If A given B.
mutually exclusive
When two events have no sample points in common. When one event occurs the other cannot occur.
Permutation
Which one is always greater? Permutation or combination?
Joint probability
_____ of A and B is the probability of the intersection A and B
Union
______ of events A or B is the event containing all sample points that are in A or B or both (synonymous with "or")
intersection
_______of events A and B is the event that occurs when both A and ah occur (synonymous with "and")
Probability
a numerical measure of the likelihood that an event will occur
Classical
approach to assigning probability to experimental outcomes that's based on equally likely events
Subjective
approach to assigning probability to experimental outcomes where assignment based on assignor's judgement
Relative Frequency
approach to assigning probability to experimental outcomes where assignments are based on experimental or historical data
n!/r!(n-r)!
combination formula
n!/(n-r)!
permutation formula
multiplication law
provides way to compute the probability of the intersection of two events.