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

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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

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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

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0.794

Course 3

10-1Probability

Course 3

10-1Probability

Ticket Out:

What is the difference between an outcome and an event?