Probability Calculates the likelihood an event will occur
• Must lie between 0 and 1• “0” implies that the event will not occur• “1” implies that the event will definitely occur
Probability of an Event: P(A)
Sample Space: The set of all possible outcomes of an experiment
Example: You are rolling two dice, what is the sample space?
Sample Space: The set of all possible outcomes of an experiment
Example: picking a card, what is the sample space?
• 52 cards• 13 cards in each suits• 12 face cards• 4 suits:
6.5
Example• What is the probability of each of the events
occurring when rolling two dice?
1) P(they add up to 2) = ?• P(2) = 1/36
2) P(6) = ?• P(6) = 5/36
3) P(10) = ?• P(10) = 3/36
Independent Events: the occurrence of one does not affect the probability of the other
Multiplication Rule Finding the probability of more than one event.
The word “AND” is always used when describing the situation.
1) P(rolling a 4 and then a 2) = 1/6 *1/6 = 2.8%2) P(rolling three odd numbers in a row) = 3/6*3/6*3/6=12.5%
Multiplication Rule for Independent Events
P(A and B) = P(A) * P(B)
Example: What is the probability of rolling five 6’s in a row on a six sided die.
P(6&6&6&6&6) = (1/6) (1/6) (1/6) (1/6) (1/6)= 0.0001
P(A and B) = P(A) * P(B)
Example:
There are 11 marbles in a bag.
2 yellow, 5 pink, 4 green
You pull out one marble and put it back in the bag and then pull out another marble. What is the probability of picking pink twice in a row
P(pink and pink) = (5/11)*(5/11) = 25/121 = 21%
Multiplication Rule for Independent Events
What is the probability of getting heads on a coin flip AND picking a brown ball out of a bag?
P(heads and blue ball) Option #1: Multiply the probability of heads and brown ball: 1/3*1/2
Option #2:a) find the size of
the sample space
b) count the outcome of interest
c) Use results from a and b to find the probability
Compliment of an Event
If A is an event within the sample space S of an activity or experiment, the complement of A (denoted A') consists of all outcomes in S that are not in A.
The complement of A is everything else in the problem that is NOT in A.
Complement:P(A') = 1 - P(A)
