counting outcomes and theoretical probability pre-algebra lesson 12-4 (for help, go to lesson 6-4.)...
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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
Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical ProbabilityPRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4
Solutions
1.
2.
3.
4.
5.
6.
favorable outcomesall possible outcomes =
drawing a blue chip12 =
512
13
412
favorable outcomesall possible outcomes =
drawing a red chip12 = =
favorable outcomesall possible outcomes =
drawing a chip that is not red12 =
812 =
23
favorable outcomesall possible outcomes =
drawing a red or blue chip12 =
912 =
34
favorable outcomesall possible outcomes =
drawing a tan chip12 =
312 =
14
favorable outcomesall possible outcomes =
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?
PRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4
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
Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical ProbabilityPRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 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
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5
Solutions
1. 2. 3.
4. 5. 6. 518
325
2072 =
18
216 =
27
1242 =
45
7290 =
8100
225=
12-5
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 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?
PRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5
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
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-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?
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
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 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?