10-6 Making Decisions and Predictions
Warm Up
Problem of the Day
Lesson Presentation
Course 3
10-6 Making Decisions and Predictions
Warm Up
Solve each proportion.
6
x
1. 5.1 = 1.7
18
65
13
3. 0.1 = x
46
200
0.02 4. n = 46
Course 3
24
n
2. 108 = 9
2
10.58
10-6 Making Decisions and Predictions
Problem of the Day
Aiden is playing a board game using two
six-sided number cubes. He wins if he
doesn’t roll a six or a seven. What is the
probability that Aiden will win on his
next turn?
25
36
Course 3
10-6 Making Decisions and Predictions
Learn to use probability to make decisions
and predictions.
Course 3
10-6 Making Decisions and Predictions
Additional Example 1A: Using Probability to Make
Decisions and Predictions
The table shows the satisfaction rating in a
business’s survey of 500 customers. Of their
240,000 customers, how many should the
business expect to be unsatisfied?
Pleased
Satisfied
Unsatisfied
125
340
35
Find the probability of unsatisfied customers in the
survey.
number of customers unsatisfied in survey
35
7
=
or
total number of customers surveyed
500 100
Course 3
10-6 Making Decisions and Predictions
Additional Example 1A Continued
7 = t n t
100
240,000
7 x 240,000 = 100n
1,680,000 = 100n
t 100
100
Set up a proportion.
Find the cross products.
Divide both sides by 100.
16,800 = n
The business should expect to have 16,800 unsatisfied
customers.
Course 3
10-6 Making Decisions and Predictions
Additional Example 1B: Using Probability to Make
Decisions and Predictions
Jared randomly draws a card from a 52-card
deck and tries to guess what it is. If he tried
this trick 1040 times over the course of his
life, what is the best prediction for the amount
of times it works?
Find the theoretical probability of successful trick
attempts.
number of possible outcomes = 1
total possible outcomes
52
Course 3
10-6 Making Decisions and Predictions
Additional Example 1B Continued
1 =t n t
52
1040
Set up a proportion.
1  1040 = 52n
Find the cross products.
1040 = 52n
t 52
52
Divide both sides by 52.
20 = n
The trick would work about 20 times.
Course 3
10-6 Making Decisions and Predictions
Check It Out: Example 1A
The table shows the satisfaction rating in a
business’s survey of 500 customers. Of their
240,000 customers, how many should the
business expect to be pleased?
Pleased
Satisfied
Unsatisfied
125
340
35
Find the probability of pleased customers in the
survey.
number of customers pleased in survey
125
1
=
or
total number of customers surveyed
500
4
Course 3
10-6 Making Decisions and Predictions
Check It Out: Example 1A Continued
1 = t n t
4
240,000
1  240,000 = 4n
240,000 = 4n
t 4
4
Set up a proportion.
Find the cross products.
Divide both sides by 4.
60,000 = n
The business should expect to have 60,000 please
customers.
Course 3
10-6 Making Decisions and Predictions
Check It Out: Example 1B
Kaitlyn randomly draws a domino tile from an
18 piece set and tries to guess what it is. If
she tries this trick 2250 times over the course
of her life, what is the best prediction for the
amount of times it works?
Find the theoretical probability of successful trick
attempts.
number of possible outcomes = 1
total possible outcomes
18
Course 3
10-6 Making Decisions and Predictions
Check It Out: Example 1B Continued
1 =t n t
18
2250
Set up a proportion.
1 x 2250 = 18n
Find the cross products.
2250 = 18n
t 18
18
Divide both sides by 18.
125 = n
Approximately 125 times the trick would work.
Course 3
10-6 Making Decisions and Predictions
Additional Example 2: Deciding Whether a Game is
Fair
In a game, two players each flip a coin. Player
A wins if exactly one of the two coins is heads.
Otherwise, player B wins. Determine whether
the game is fair.
List all possible outcomes.
HH HT TT TH
Find the theoretical probability of each player’s
winning.
P(player A winning) = 1 There are 2 possibilities
2 with exactly 1 coin as
1 heads.
P(player B winning) =
2
1 1
Since 2 = 2 , the game is fair.
Course 3
10-6 Making Decisions and Predictions
Check It Out: Example 2
In a new game, two players each flip a coin.
Player A wins if at least one of the two coins is
heads. Otherwise, player B wins. Determine
whether the game is fair.
List all possible outcomes.
HH HT TT TH
Find the theoretical probability of each player’s
winning.
P(player A winning) = 3 There are 3 possibilities
4 with at least 1 coin as
1 heads.
P(player B winning) =
4
1 3
Since 4 ≠ 4 , the game is not fair.
Course 3
Decisions
and
Predictions
10-6 Making
Insert Lesson
Title
Here
Lesson Quiz: Part I
1. Out of the 35 products a salesperson sold last
week, 8 of them were products worth over
$200. About how many of these products
should the salesperson expect to sell if he has
140 customers next month? 32
2. A student answers all 12 multiple choice
questions on a quiz at random. Each multiple
choice question has 4 choices. What is the best
guess for the amount of multiple choice
questions the student will answer correctly? 3
Course 3
Decisions
and
Predictions
10-6 Making
Insert Lesson
Title
Here
Lesson Quiz: Part II
3. In a game, two players each roll a 6-sided
number cube and add the two numbers. If the
roll is a 6 or less, player A wins. If the roll is 8
or more, player B wins. if the roll is a 7, the
players tie and roll again. Is this a fair game?
Yes
Course 3