Download Vocabulary: Experiment: Sample Space: Event: The Probability of an

Section 2.1 ­ Probability
Flip a coin:
Probability of observing Heads =
Roll one die:
Probability a prime number shows =
Spin the spinner: Probability it lands on red =
Vocabulary:
Experiment:
Sample Space:
Event:
The Probability of an event:
The Probability of the sample space:
Example:
An experiment consists of rolling one die and then flipping one coin.
Example continued...
Sample Space = {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}
A = {1H, 2H, 3H, 4H, 5H, 6H}
B = {6H, 6T}
C = {1T, 2T, 3T, 4T, 5T, 6T}
(1) Find the probability events A and C occur at the same time.
(2) Find the probability events A and B occur at the same time.
(3) Find the probability event B does NOT occur.
We can create new events by combine other events.
Let A and B represent events.
A and B
A or B
A∩B =∅
Not A
Example: Suppose P(A) = 0.5 and P(B)=0.4.
(1) If events A and B are mutually exclusive, then find P(A ∪ B).
(2)
If the probability events A and B happen at the same time is 0.1,
then find P(A ∪ B).
(3) Find the probability event B does not occur.
Summary:
Let A and B be events
P(A) + P(Ac) =
P(Ac) =
P(A) =
If A and B are mutually exclusive, then
P(A∩B) =
P(A∪B) =
If A and B can occur at the same time then P(A∩B)≠0, so
P(A∪B) =
Example: Roll two dice.
Example:
A die is constructed so that a 6 occurs twice as often as a 5, which
occurs three times as often as a 1, 2, 3, or 4. Roll the die once.
List the Sample Space:
Find the probability of observing each outcome in the sample space:
P(observe a 5)
P(observe a number less than 5)