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.