Probability Facts

Question 1

Random Process

Answer 1

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

Question 2

Outcomes

Answer 2

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 ).

Question 3

Event

Answer 3

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

Question 4

Mutually Exclusive

Answer 4

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.

Question 5

Probability Measure (P)

Answer 5

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

Question 6

Conditional Probability

Answer 6

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

Question 7

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

Answer 7

P(A\B=P(A)

Question 8

Addition Rule

Answer 8

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

Question 9

Multiplication Rule

Answer 9

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

Question 10

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

Answer 10

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

Question 11

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

Answer 11

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

Question 12

Other Probability Facts

Answer 12

0 ≤ P (A) ≤ 1

P ( Ω ) = 1

Question 13

The Law of Total Probability:

Answer 13

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….