3-1,3-2, 3-3,3-4
Experiment – the activity taking place – EX: rolling dice, drawing cards, flipping
coins, etc.
Outcome - What might happen when an experiment takes place - Ex: rolling a three,
drawing an Ace of Hearts, tails on a coin, etc.
Sample space - the set of all possible outcomes
Event – A subset of the possible outcomes that contains the desired outcomes
Probability of an event P(E) = number of ways that event may occur
total number of all possible outcomes
Equally likely outcomes; No outcome is more likely to occur than any
other possible outcome.
The complement of event A, denoted A , consists of all outcomes in which event A does not
occur.
P(not A) =
__________________
A. Roll one die List the sample space:
Find each probability:
P(4) =
P (not 4) =
P(7) =
P(number less than 7) =
P(odd) =
The probability of an impossible event is ______.
The probability of an event that is certain to occur is _______.
If a year is selected at random, find the probability that Thanksgiving Day will be on a (a)
Wednesday , (b) Thursday .
Every probability is a number between 0 and 1 .
P(A or B) = P(event A occurs or event B occurs or they both occur)
Use the data in the following table, which summarizes results from the sinking of the Titanic.
Survived
Died
Men
332
1360
Women
318
104
Boys
29
35
Girls
27
18
If one person is randomly selected, find the probability :
1. P(women or a child) =
3. P( a child or someone who
survived)
2. P( a man or someone who survived)=
P(A and B) = P(event A occurs in a first trial and event B occurs in a second trial)
Two cards are to be drawn with replacement.
P(Ace and king) =
P(Ace and Ace) =
P(Ace and not Ace) =
P(club and spade) =
Two cards are to be drawn without replacement.
P(Ace and king) =
P(Ace and Ace) =
P(Ace and not Ace) =
P(club and spade) =
Notation for Conditional Probability:
P( B A) represents the probability of event B occurring after it is assumed
that event A has already occurred.
Given that Event 2 has occurred, you must make an adjustment to you sample
space. The size of the sample space (total number of outcomes) will be reduced
based on the knowledge that E2 has occurred. Conditional probability is written
P(E1|E2) - read probability of E1 given E2.
Examples:
1. Using tree diagrams: A family plans to have three children. Make a tree
diagram for the sample space. Determine the following probabilities:
P(at least two girls)
P(at least two girls|the first child is a girl)
P(exactly two boys)
P(exactly two boys|at least one boy).
P(three girls)
P(three girls|first child is a girl)
2. Using a chart: A recent survey of Chipola students indicates the following
results for type of soda preferred :
Regular Cola
Diet Cola
No Cola
Freshmen
40
30
15
Sophomores
30
30
20
Determine the following probabilities:
P(cola)
P(freshman)
P(freshman or prefers cola)
P(freshman and prefers cola)
P(prefer regular cola|freshman)
P(diet cola|sophomore)
P(sophomore|prefer diet cola)
Homework : Do Statistics Worksheet – Review of Probability