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Flashcards in Probability Facts Deck (13):
1

Random Process

Is the process that has unpredictable result.
e.g. rolling the dice.
This can also be called an experiment.

2

Outcomes

Are all possible results.
e.g. 1, 2, 3, 4, 5, 6.
We use the Greek letter Ω to mean the set of all possible outcomes.
e.g. Ω = ( 1, 2, 3, 4, 5, 6 ).

3

Event

Is a set of outcomes.
e.g. { 2, 4, 6 }
When we say an event has occurred, we mean that the random process resulted in one of the outcomes of the event.
e.g. 2, 4, or 6

4

Mutually Exclusive

Two events are mutually exclusive if they have no outcomes in common.
e.g. { 1, 2} and {4, 5}
These events can also be called disjoint.

5

Probability Measure (P)

Rule or table that gives the probability of every event. Usually we use upper case letter P for the probability measure.

We write the probabilities of events like this:
P({2, 4, 6 }) = 0.5 or sometimes as a shortcut: P(A) = 0.5

6

Conditional Probability

The Conditional Probability of event A given event B is:
P(A/B) = P(A and B)
_________
P(B)

7

If we say the two events are INDEPENDENT, this means?

P(A\B=P(A)

8

Addition Rule

P ( A or B ) = P (A) + P (B) - P ( A and B)

9

Multiplication Rule

P( A and B ) = P(A)P(BIA)

10

If events A and B are independent, then the multiplication rule becomes what?

P ( A and B ) = P (A)P (B)

11

If A and B are mutually exclusive then the addition rule becomes...

P ( A or B ) = P ( A ) + P ( B )

12

Other Probability Facts

0 ≤ P (A) ≤ 1
P ( Ω ) = 1

13

The Law of Total Probability:

If events X1, X2, and X3 are mutually exclusive and have probabilities that add up to one, then for any event A:
P (A) = P(AIX1)P(X1) + P(AIX2)P(X2) + P(AIX3)P(X3)
* this is also true for any other number of events:
X1, X2, X3, X4....