10-1 Probability
Course 3
Warm Up
Problem of the Day
Lesson Presentation
Warm UpWrite each fraction in simplest form.
1. 2.
3. 4.
Course 3
10-1Probability
1620
1236
864
39195
4
5
1
3
1
8
1
5
Problem of the Day
A careless reader mixed up some encyclopedia volumes on a library shelf. The Q volume is to the right of the X volume, and the C is between the X and D volumes. The Q is to the left of the G. X is to the right of C. From right to left, in what order are the volumes?D, C, X, Q, G
Course 3
10-1Probability
Learn to find the probability of an event by using the definition of probability.
Course 3
10-1Probability
Vocabularyexperimenttrialoutcomesample spaceeventprobabilityimpossiblecertain
Insert Lesson Title Here
Course 3
10-1Probability
Course 3
10-1Probability
An experiment is an activity in which results are observed. Each observation is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment.
Experiment Sample Space
flipping a coin heads, tails
rolling a number cube 1, 2, 3, 4, 5, 6
guessing the number of whole numbers marbles in a jar
Course 3
10-1Probability
An event is any set of one or more outcomes. The probability of an event, written P(event), is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen.
• A probability of 0 means the event is impossible, or can never happen.
• A probability of 1 means the event is certain, or has to happen.
• The probabilities of all the outcomes in the sample space add up to 1.
Course 3
10-1Probability
0 0.25 0.5 0.75 1
0% 25% 50% 75% 100%
Never Happens about Alwayshappens half the time happens
14
12
340 1
Give the probability for each outcome.
Additional Example 1A: Finding Probabilities of Outcomes in a Sample Space
Course 3
10-1Probability
The basketball team has a 70% chance of winning.
The probability of winning is P(win) = 70% = 0.7. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.7 = 0.3, or 30%.
Give the probability for each outcome.
Additional Example 1B: Finding Probabilities of Outcomes in a Sample Space
Course 3
10-1Probability
Three of the eight sections of the spinner are labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is
P(1) = .38
Additional Example 1B Continued
Course 3
10-1Probability
Three of the eight sections of the spinner are labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P(2) = .3
8
Two of the eight sections of the spinner are labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P(3) = = .2
814
Check The probabilities of all the outcomes must add to 1.
38
38
28
++ = 1
Give the probability for each outcome.
Check It Out: Example 1A
Course 3
10-1Probability
The polo team has a 50% chance of winning.
The probability of winning is P(win) = 50% = 0.5. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.5 = 0.5, or 50%.
Give the probability for each outcome.Check It Out: Example 1B
Course 3
10-1Probability
Rolling a number cube.
One of the six sides of a cube is labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is P(1) = . 1
6
Outcome 1 2 3 4 5 6
Probability
One of the six sides of a cube is labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P(2) = . 1
6
Check It Out: Example 1B Continued
Course 3
10-1Probability
One of the six sides of a cube is labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P(3) = . 1
6
One of the six sides of a cube is labeled 4, so a reasonable estimate of the probability that the spinner will land on 4 is P(4) = . 1
6
One of the six sides of a cube is labeled 5, so a reasonable estimate of the probability that the spinner will land on 5 is P(5) = . 1
6
Check It Out: Example 1B Continued
Course 3
10-1Probability
One of the six sides of a cube is labeled 6, so a reasonable estimate of the probability that the spinner will land on 6 is P(6) = . 1
6
Check The probabilities of all the outcomes must add to 1.
16
16
16
++ = 116
+16
+16
+
Course 3
10-1Probability
To find the probability of an event, add the probabilities of all the outcomes included in the event.
A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
Additional Example 2A: Finding Probabilities of Events
Course 3
10-1Probability
What is the probability of guessing 3 or more correct?
The event “three or more correct” consists of the outcomes 3, 4, and 5.
P(3 or more correct) = 0.313 + 0.156 + 0.031 = 0.5, or 50%.
Course 3
10-1Probability
What is the probability of guessing fewer than 2 correct?
The event “fewer than 2 correct” consists of the outcomes 0 and 1.
P(fewer than 2 correct) = 0.031 + 0.156 = 0.187, or 18.7%
Additional Example 2B: Finding Probabilities of EventsA quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
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10-1Probability
What is the probability of passing the quiz (getting 4 or 5 correct) by guessing?
The event “passing the quiz” consists of the outcomes 4 and 5.
P(passing the quiz) = 0.156 + 0.031 = 0.187, or 18.7%
Additional Example 2C: Finding Probabilities of EventsA quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
Check It Out: Example 2A
Course 3
10-1Probability
What is the probability of guessing 2 or more correct?
The event “two or more correct” consists of the outcomes 2, 3, 4, and 5.
P(2 or more) = 0.313 + 0.313 + 0.156 + 0.031 = .813, or 81.3%.
Course 3
10-1Probability
What is the probability of guessing fewer than 3 correct?
The event “fewer than 3” consists of the outcomes 0, 1, and 2.
P(fewer than 3) = 0.031 + 0.156 + 0.313 = 0.5, or 50%
Check It Out: Example 2BA quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
Course 3
10-1Probability
What is the probability of passing the quiz with all 5 correct by guessing?
The event “passing the quiz” consists of the outcome 5.
P(passing the quiz) = 0.031 = or 3.1%
Check It Out: Example 2CA quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
Additional Example 3: Problem Solving Application
Course 3
10-1Probability
Six students are in a race. Ken’s probability of winning is 0.2. Lee is twice as likely to win as Ken. Roy is as likely to win as Lee. Tracy, James, and Kadeem all have the same chance of winning. Create a table of probabilities for the sample space.
14
Additional Example 3 Continued
Course 3
10-1Probability
1 Understand the Problem
The answer will be a table of probabilities. Each probability will be a number from 0 to 1. The probabilities of all outcomes add to 1.
List the important information:
• P(Ken) = 0.2
• P(Lee) = 2 P(Ken) = 2 0.2 = 0.4
• P(Tracy) = P(James) = P(Kadeem)
• P(Roy) = P(Lee) = 0.4 = 0.1 14
14
Additional Example 3 Continued
Course 3
10-1Probability
2 Make a Plan
You know the probabilities add to 1, so use the strategy write an equation. Let p represent the probability for Tracy, James, and Kadeem.
P(Ken) + P(Lee) + P(Roy) + P(Tracy) + P(James) + P(Kadeem) = 1
0.2 + 0.4 + 0.1 + p + p + p = 1
0.7 + 3p = 1
Course 3
10-1Probability
Solve3
0.7 + 3p = 1
–0.7 –0.7 Subtract 0.7 from both sides.
3p = 0.3
3p3
0.33
= Divide both sides by 3.
Additional Example 3 Continued
p = 0.1
Course 3
10-1Probability
Look Back4
Check that the probabilities add to 1.
0.2 + 0.4 + 0.1 + 0.1 + 0.1 + 0.1 = 1
Additional Example 3 Continued
Four students are in the Spelling Bee. Fred’s probability of winning is 0.6. Willa’s chances are one-third of Fred’s. Betty’s and Barrie’s chances are the same. Create a table of probabilities for the sample space.
Check It Out: Example 3
Course 3
10-1Probability
Check It Out: Example 3 Continued
Course 3
10-1Probability
1 Understand the Problem
The answer will be a table of probabilities. Each probability will be a number from 0 to 1. The probabilities of all outcomes add to 1.
List the important information:
• P(Fred) = 0.6
• P(Betty) = P(Barrie)
• P(Willa) = P(Fred) = 0.6 = 0.213
13
Check It Out: Example 3 Continued
Course 3
10-1Probability
2 Make a Plan
You know the probabilities add to 1, so use the strategy write an equation. Let p represent the probability for Betty and Barrie.
P(Fred) + P(Willa) + P(Betty) + P(Barrie) = 1
0.6 + 0.2 + p + p = 1
0.8 + 2p = 1
Course 3
10-1Probability
Solve3
0.8 + 2p = 1
–0.8 –0.8 Subtract 0.8 from both sides.
2p = 0.2
Check It Out: Example 3 Continued
Outcome Fred Willa Betty Barrie
Probability 0.6 0.2 0.1 0.1
p = 0.1
Course 3
10-1Probability
Look Back4
Check that the probabilities add to 1.
0.6 + 0.2 + 0.1 + 0.1 = 1
Check It Out: Example 3 Continued
Lesson Quiz
Use the table to find the probability of each event.
1. 1 or 2 occurring
2. 3 not occurring
3. 2, 3, or 4 occurring
0.874
0.351
Insert Lesson Title Here
0.794
Course 3
10-1Probability
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