Transcript Lesson 12.4 and 12.5 - Crestwood Local Schools

Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
(For help, go to Lesson 6-4.)
A bag has 5 blue (B) chips, 4 red (R) chips, and 3 tan (T) chips.
Find each probability for choosing a chip at random from the bag.
1. P(R)
2. P(not R)
3. P(B)
4. P(R or B)
5. P(T)
6. P(B or T)
Check Skills You’ll Need
12-4
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
Solutions
1.
favorable outcomes
drawing a red chip
4
1
=
=
=
all possible outcomes
12
12
3
2.
favorable outcomes
drawing a chip that is not red
8
2
=
=
=
all possible outcomes
12
12 3
3.
favorable outcomes
drawing a blue chip
5
=
=
all possible outcomes
12
12
favorable outcomes
4. all possible outcomes =
drawing a red or blue chip
9
3
=
=
12
12
4
5.
favorable outcomes
drawing a tan chip
3
1
=
=
=
all possible outcomes
12
12
4
6.
favorable outcomes
drawing a blue or tan chip
8
2
=
=
=
all possible outcomes
12
12
3
12-4
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
The school cafeteria sells sandwiches for which you can choose
one item from each of the following categories: two breads (wheat or
white), two meats (ham or turkey), and two condiments (mayonnaise or
mustard). Draw a tree diagram to find the number of sandwich choices.
ham
wheat
turkey
ham
white
turkey
mayonnaise
mustard
mayonnaise
mustard
mayonnaise
mustard
mayonnaise
mustard
There are 8 possible sandwich choices.
12-4
Each branch of the “tree”
represents one choice—for
example, wheat-hammayonnaise.
Quick Check
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
In some state lotteries, the winning number is made up of five
digits chosen at random. Suppose a player buys 5 tickets with different
numbers. What is the probability that the player has a winning number?
First find the number of possible outcomes. For each digit, there are 10
possible outcomes, 0 through 9.
1st digit
2nd digit
3rd digit
4th digit
5th digit
outcomes outcomes outcomes outcomes outcomes
•
•
•
•
10
10
10
10
10
total
outcomes
= 100,000
Then find the probability when there are five favorable outcomes.
number of favorable outcomes
5
P(winning number) = number of possible outcomes = 100,000
The probability is
5
1
, or
.
100,000
20,000
12-4
Quick Check
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
Use the following information for Questions 1 and 2. In a game, a number
cube is tossed to determine the number of spaces to move, and a coin is
tossed to determine forward or backward movement.
1. How many possible outcomes are there?
12
2. What is the theoretical probability you will move four spaces?
1
6
3. How many different three-digit whole numbers are possible using the
digits 1, 2, 3, 4, and 5?
125
12-4
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
(For help, go to Lesson 5-4.)
Multiply.
1.
3 1
•
5 5
4. 5 • 4
9
8
2.
1 2
•
4 4
5. 4 • 3
7
6
3.
4
2
•
10
10
6. 9 • 8
10
9
Check Skills You’ll Need
12-5
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Solutions
3
20
2
1
12
2
2. 16 = 8
1. 25
5
4. 72 = 18
5. 42 = 7
12-5
8
2
3. 100 = 25
72
4
6. 90 = 5
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Quick Check
You roll a number cube once. Then you roll it again. What is the
probability that you get 5 on the first roll and a number less than 4 on the
second roll?
P(5) =
1
6
There is one 5 among 6 numbers on a number cube.
P(less than 4) =
3
6
There are three numbers less than 4 on a number cube.
P(5, then less than 4) = P(5) • P(less than 4)
1
3
= 6 • 6
=
3
1
, or
36
12
The probability of rolling 5 and then a number less than 4 is 1 .
12
12-5
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Three girls and two boys volunteer to represent their class at a
school assembly. The teacher selects one name and then another from a
bag containing the five students’ names. What is the probability that both
representatives will be boys?
P(boy) =
2
5
Two of five students are boys.
P(boy after boy) =
1
4
If a boy’s name is drawn, one of the four
remaining students is a boy.
P(boy, then boy) = P(boy) • P(boy after boy)
2
1
= 5 • 4
=
2
1
, or
20
10
Substitute.
Simplify.
The probability that both representatives will be boys is
12-5
1
.
10
Quick Check
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Solve.
1. You roll a number cube once. Then you roll it again. What is the
probability that you get 6 on the first roll and a number greater than 3
on the second roll?
1
12
2. Suppose there are three white marbles and three black marbles in a
bag and you want to remove two marbles. What is the probability that
you will select a white marble and then a black marble? Express your
answer as a percent.
30%
12-5
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Solve.
3.
Each of five girls and seven boys wants to be one of the two
announcers for a variety show. To be fair, a teacher puts the
names of the twelve students in a hat and draws two. What
is the probability that the teacher will draw the names of two
boys? Of two girls?
7
; 5
22 33
12-5