Transcript Chapter 6 Lesson 9 Probability and Predictions pgs. 310-314

Chapter 6 Lesson 9
Probability and Predictions
pgs. 310-314
What you’ll learn:
Find the probability of simple
events
Use a sample to predict the
actions of a larger group
Vocabulary


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Outcomes (310): results of a probability
problem
Simple Event (310): one outcome or a
collection of outcomes
Probability (310): the chances of an event
happening
Sample Space (311): the set of all possible
outcomes
Theoretical Probability (311): what should
occur
Experimental Probability (311): what actually
occurs when conducting a probability
experiment
Key Concept (310):
Probability
Words: The probability of an event is a
ratio that compares the number of
favorable outcomes to the number
of possible outcomes.
Symbols: P(event) = number of favorable outcomes
number of possible outcomes
The probability of an event is always between 0 and 1, inclusive.
The closer a probability is to 1, the more likely it is to occur.
Example 1: Find Probability
Ten cards are numbered 1 through 10, and one card is
chosen at random. Determine the probability of
drawing an even number.
What we know: There are 10 cards
We also know that 2,4,6,8,10 are even numbers.
There are 10 possible outcomes: 1,2,3,4,5,6,7,8,9,10
P(even) = number of favorable outcomes
number of possible outcomes
P(even) = 5 = 1
10 2
So the probability of drawing an even number
Is 1 or 50%.
2
In Example 1, the set of all possible
outcomes is called the sample
space.
What was the sample space for
example 1?
{1,2,3,4,5,6,7,8,9,10} notice the sample space
is in brackets
Example 2: Find Probability
1
2
3
4
5
6
1
2
3
4
(1,1)
(2,1)
(3,1)
(4,1)
(1,2)
(2,2)
(3,2)
(4,2)
(1,3)
(2,3)
(3,3)
(4,3)
(1,4)
(2,4)
(3,4)
(4,4)
(1,5)
(2,5)
(3,5)
(4,5)
(1,6)
(2,6)
(3,6)
(4,6)
5
6
(5,1)
(6,1)
(5,2)
(6,2)
(5,3)
(6,3)
(5,4)
(6,4)
(5,5)
(6,5)
(5,6)
(6,6)
These are all the possible outcomes of rolling 2 dice, each
with the numbers 1-6. This is the sample space.
Pg. 311
Refer to the previous chart
P(event) = Number of favorable outcomes
Number of possible outcomes

Suppose two dice are rolled. Find
the probability of rolling an odd sum.
Take a look at the sample space, add all the
sums Ex. (1,2) = 3 and count how many
are odd
There are 18 outcomes in which the sum is odd.
So, P(odd)= 18 = 1 = 50%
36 2
This means there is a 50% chance of rolling an odd sum.
The Probabilities in Example 1 & 2 are
Theoretical Probability---what should happen

Example 3: Find Experimental
Probability (what actually occurs)
Outcome
Tally
Heads
Tails
IIII IIII IIII
IIII IIII I
Frequency
14
11
This table shows the results of an experiment in which a coin was
Tossed. Find the experimental probability of tossing a coin and
getting tails for this experiment.
The experimental
Number of times tails occur = 11 = 11
Number of possible outcomes 14+11 25
Probability of getting
Tails in this case is 11
25
or 44%
Example 4: Make a Prediction
Mary took a sample from a package of
jellybeans and found that 30% of the beans
were red. Suppose there are 250 jellybeans
in the package. How many can she expect to
be red?
The total number of jellybeans is 250, so 250 is the base.
The percent is 30%.
You can choose to use the percent proportion or the percent
equation. Let’s look at both ways.
Percent Proportion Way:

Mary took a sample from a package of
jellybeans and found that 30% of the
beans were red. Suppose there are
250 jellybeans in the package. How
many can she expect to be red?
The total number of jellybeans is 250, so 250 is the base.
The percent is 30%.
n = 30
250 100
100n = 25030
100n = 7500
100n = 7500
100
100
n = 75
So, Mary could
Expect 75 of the
Jellybeans to be red.
Percent Equation Way:

Mary took a sample from a package of
jellybeans and found that 30% of the
beans were red. Suppose there are
250 jellybeans in the package. How
many can she expect to be red?
The total number of jellybeans is 250, so 250 is the base.
The percent is 30%.
Part = Percent Base
n = .30(250)
n = 75
So, as you can see that by using
Either formula, Mary could
Expect 75 of the jellybeans to be
Red.
Your Turn!
There are 4 blue marbles, 6 red marbles, 3 green
marbles, and 2 yellow marbles in a bag. Suppose
you select one marble at random. Find the
probability of each out come. Express each
probability as a fractions and as a percent. Round
to the nearest percent.
A.
B.
P(green)
P(green) = 3 = 1 = 20%
15
5
P(red or yellow)
P(red or yellow) = 8 ; 53%
15
Your Turn Again!
Suppose two number cubes are rolled. What is the
probability of rolling a sum greater than 8?
Refer to the sample space on pg. 311.
10 = 5 ; about 28%
36 18
A sample from a package of assorted cookies revealed
That 20% of the cookies were sugar cookies. Suppose
there are 45 cookies in the package. How many can be
expected to be sugar cookies?
n = 20
45 100
n100 = 4520
100n = 900
n=9
n = .20(45)
OR
n=9
Using either formula, you could
expect 9 cookies to be sugar.
Quiz over 6-8 & 6-9
tomorrow!
We will be reviewing on
Thursday and testing on
Friday over Chapter 6.