Counting Outcomes and Theoretical Probability PRE-ALGEBRA LESSON 12-4 (For help, go to Lesson 6-4.)...

Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical ProbabilityPRE-ALGEBRA LESSON 12-4PRE-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


Solutions

1.

2.

3.

4.

5.

6.

favorable outcomesall possible outcomes =

drawing a blue chip12 =

512

13

412


drawing a red chip12 = =


drawing a chip that is not red12 =

812 =

23


drawing a red or blue chip12 =

912 =

34


drawing a tan chip12 =

312 =

14


drawing a blue or tan chip12 =

812 =

23

12-4

Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical Probability

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.

PRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4

There are 8 possible sandwich choices.

mayonnaise

Each branch of the “tree” represents one choice—for example, wheat-ham-mayonnaise.

wheat

white

ham

turkey

ham

turkey

mayonnaisemustardmayonnaisemustardmayonnaisemustard

mustard

Quick Check

12-4

Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical Probability

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 digitoutcomes

10

2nd digitoutcomes

10

3rd digitoutcomes

10

5th digitoutcomes

10

4th digitoutcomes

10

totaloutcomes= 100,000• • • •

Then find the probability when there are five favorable outcomes.

P(winning number) = =number of favorable outcomesnumber of possible outcomes

5100,000

5100,000

The probability is , or .120,000 Quick Check

12-4


Use the following information for Questions 1 and 2. In a game, a numbercube is tossed to determine the number of spaces to move, and a coin istossed to determine forward or backward movement.

1. How many possible outcomes are there?

2. What is the theoretical probability you will move four spaces?

3. How many different three-digit whole numbers are possible using the digits 1, 2, 3, 4, and 5?

125

12

16

12-4

Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5

(For help, go to Lesson 5-4.)

Multiply.

1. • 2. • 3. •

4. • 5. • 6. •

35

15

14

24

47

36

59

48

410

210

910

89

Check Skills You’ll Need

12-5


Solutions

1. 2. 3.

4. 5. 6. 518

325

2072 =

18

216 =

27

1242 =

45

7290 =

8100

225=

12-5


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?

The probability of rolling 5 and then a number less than 4 is .112

P(5, then less than 4) = P(5) • P(less than 4)

= •16

36

336

112

= , or

P(5) =16 There is one 5 among 6 numbers on a number cube.

P(less than 4) =36 There are three numbers less than 4 on a number cube.

Quick Check

12-5

Independent and Dependent EventsIndependent and Dependent Events

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, then boy) = P(boy) • P(boy after boy)

The probability that both representatives will be boys is .110

220

110

= , or Simplify.

= •25

14

Substitute.

P(boy after boy) =14

If a boy’s name is drawn, one of the four remaining students is a boy.

P(boy) =25 Two of five students are boys.

Quick Check

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?

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%

112

12-5


Solve.

722

533

;

12-5

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?

Counting Outcomes and Theoretical Probability PRE-ALGEBRA LESSON 12-4 (For help, go to Lesson 6-4.)...

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