Chapter 3 Probability
Probability 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
Experiment
Toss a coin
Roll a die
Answer a true-false question
Toss two coins
Sample Space
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.
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 .
___________1. For a card drawn from an ordinary deck, find the probability of getting a queen.
___________ 2. If a family has three children, find the probability that all three are girls.
3. A card is drawn from an ordinary deck. Find these probabilities.
_______ a. Of getting a jack
________ b. of getting the 6 of clubs
Empirical Probability
Hospital records indicated that maternity patients stayed in the hospital for the number of days
shown in the distribution.
Number of Days Stayed
3
4
5
6
7
Frequency
15
32
56
19
5
Find these probabilities.
a. A patient stayed exactly 5 days
c. A patient stayed at most 4 days
b. A patient stayed less than 6 days
d. A patient stayed at least 5 days
Addition Rules for Probability
Consider you are at a large political gathering and you select a person at
random, and you wish to know if that person is a female or a Republican.
There are three possibilities:
1.
2.
3.
Consider you wish to know if a person is Republican or Democrat.
In this case, there are only two possibilities:
1.
2.
Two events are mutually exclusive if they cannot occur at the same time.
Determine which events are mutually exclusive and which are not when a single
card is drawn from a deck.
(A) Getting a 7 and getting a jack.
(B) Getting a club and getting a king.
(C) Getting a face card and getting an ace.
(D) Getting a face card and getting a spade.
Mutually exclusive: P( A or B) = P(A) + P(B)
1. A drawer contains three pairs of red socks, two pairs of black socks, and four
pairs of brown socks. If a person in a dark room selects a pair of socks, find the
probability that the pair will be either black or brown.
2. A day of the week is selected at random. Find the probability that it is a
weekend day.
Not Mutually exclusive: P(A or B) = P(A) + P(B) - P(A and B)
1. In a hospital unit there are eight nurses and five physicians. Seven nurses and
three physicians are female. If a staff person is selected, find the probability that
the subject is a nurse or a male.
2. A single card is drawn from a deck. Find the probability that it is a king or a
club.
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)=
Multiplication Rules for Probability
Two events A and B are independent if the probability of A occurring does not
affect the probability of B occurring.
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Independent Events : P(A and B) = P A  P B
1. A coin is flipped and a die is rolled. Find the probability of getting a head on
the coin and a 4 on the die.
2. A card is drawn from a deck and replaced; then a second card is drawn. Find
the probability of getting a queen and then an ace.
3. An urn contains 3 red balls, 2 blue balls, and 5 white balls. A ball is selected,
its color noted, and then it is replaced. A second ball is selected, and its color is
noted. Find the probability of each of the following.
a. Selecting 2 blue balls.
b. Selecting a blue ball and then a white ball.
c. Selecting a red ball and then a blue ball.
Two events are dependent when the outcome of the first event affects the
outcome of the second event.
1. Three cards are drawn from an ordinary deck and not replaced. Find the
probability of the following.
a. Getting three jacks.
b. Getting an ace, a king, and a queen in order.
c. Getting a club, a spade, and a heart in order.
d. Getting three clubs.