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Chapter 10 - Lesson 1
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EQ: How are the terms of probability used correctly to describe an event?
Course 3
10-1Probability
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
Vocabularyexperimenttrialoutcomesample spaceeventprobabilityimpossiblecertain
Insert Lesson Title Here
Course 3
10-1Probability
Course 3
10-1Probability
1. experiment is an activity in which results are observed.
2. Trial -Each observation
3. Outcome - each result
4. 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
5. event is any set of one or more outcomes
6. 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.
7. Impossible - probability of 0, meaning the event can never happen.
8. Certain- probability of 1, means the event 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.
Example #1
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.
Example #2
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
Give the probability for each outcome.With your partner – Example #3
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.
Example #4
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%
Example #5A 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 (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%.
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 occurring0.874
0.351
Insert Lesson Title Here
0.794
Course 3
10-1Probability
Course 3
10-1Probability
Ticket Out:
What is the difference between an outcome and an event?