Probability Flashcards
P (empty set) =
0
Probability
A probability is a function P that assigns to each event E in the sample space S a number P(E) called the probability of event E.
How do we assign probabilities?
We assign probabilities empirically or theoretically.
How do you find out empirical probability?
Through experimentation.
Relative frequency of E after n experiments
Number of times E occurred / n
As the number of experiments approaches infinity what happens?
The probability of event E equals the relative frequency of E
Experiment flow chart
Experiments to outcomes to sample space to event to probability to theoretical and empirical
What does it mean for something to be fair?
Each outcome is equally likely to occur
Additive Rule
If A and B are two events,
P(AUB) = P(A) + P(B) - P(A∏B)
Corrolary of Additive Rule
If A and B are mutually exclusive (disjoint) events,
P(AUB) = P(A) + P(B)
P(A’) =
1 - P(A)
P(A∏B’) =
P(A) - P(A∏B)
When do you use tree diagrams?
Only for conditional probability.
P(A|B) =
Probability of A given B
P(A∏B)/P(B)
Multiplication Principle for conditional probability
P(A∏B) = P(A|B)*P(B)
