12.7 probability and odds 1

Lesson 12.7, For use with pages 685-689

1. a dog 2. a cat or rabbit

An animal shelter has 12 dogs, 15 cats, 2 snakes, and 3 rabbits. Find the probability of randomly selecting an animal.

Lesson 12.7, For use with pages 685-689

1. a dog 2. a cat or rabbit

An animal shelter has 12 dogs, 15 cats, 2 snakes, and 3 rabbits. Find the probability of randomly selecting an animal.

ANSWER 38 ANSWER 9

16

Probability and Odds

Section 12.7

P. 685

Essential Questions

What are the differences between permutations and combinations?

What are the differences between odds and probability?

How is probability used to make predictions?

What are the differences between experimental and theoretical probabilities?

Vocabulary Probability:

Number of favorable outcomes

Number of possible outcomes

P (flip a head) = ½ P (flip a tail) = ½

P (flip heads or tails) = 1

P(rain) = 80% What is the probability it won’t rain?

20%

Vocabulary

Complementary: Two events are COMPLEMENTARY when one event or the other (but NOT both) must occur.

The sum of the probabilities of a complementary event is always 1.

If events A & B are complementary, the P(event A) = 1 – P(event B)

EXAMPLE 1 Finding Probabilities

Gifts

You and seven friends contribute money for a gift. Everyone’s name is put in a hat. The person whose name is chosen at random picks the gift.

a. What is the probability that your name is chosen?

b. What is the probability that your name is not chosen?

EXAMPLE 1

SOLUTION

a. P(your name is chosen) =

Number of favorableoutcomesNumber of possibleoutcomes

=18

b. P(your name is not chosen) = 1 – P(your name is

chosen).

= 1– 18

= 78

Finding Probabilities

GUIDED PRACTICE for Examples 1 and 2

You are given the probability that event A will occur. Find the probability that event A will not occur.

1. P(A) = 34

ANSWER

P(A) will not occur = 1 – P(A)

3= 1–4

=14


= 1– 0.45

= 0.55


2. P(A) = 0.45

ANSWER

P(A) will not occur = 1 – P(A)



3. P(A) = 32%

ANSWER

P(A) will not occur

= 1– 32%

= 68%

= 1 – P(A)


The 11 letters in the word MISSISSIPPI are each written on pieces of paper and randomly chosen from a bag. What is the probability of drawing an S from the bag? What is the probability of not drawing an S?

5.

P(drawings on S)

SOLUTION

= 411

Number of favorable outcomesNumber of possible outcomes=


P(Not drawings on S)

=1 – 411

=711

1 – P (drawings on S) =

Vocabulary

Odds:

Number of favorable outcomes

Number of unfavorable outcomes

Odds:

probability event will occur

probability event will NOT occur

Odds of rolling a 3 on a dice:Favorable: 3Unfavorable: 1, 2, 4, 5, 6Odds = 1/5

Odds of not rolling a 3 on a dice:Favorable: 1, 2, 4, 5, 6Unfavorable: 3Odds: 5/1

EXAMPLE 2 Finding Odds

Vacation Survey

You do a survey asking your class to rank three vacation choices Results for “the beach” are shown at the right. What are the odds in favor of a randomly chosen student from your class ranking a beach vacation first?

EXAMPLE 2

The beach was ranked first by 6 students, so thereare 6 favorable outcomes. It was ranked second by 12 students, and ranked third by 9 students, so thereare 12 +9 = 21 unfavorable outcomes.

Odds in favor Number of unfavorable outcomes

Number of favorable outcomes=

= 621

= 27

SOLUTIONFinding Odds

ANSWER

The odds in favor of a randomly chosen student ranking a beach vacation first are 2 to 7.


Odds in favor = Number of unfavorable outcomesNumber of favorable outcomes

=123

You choose a card at random from a set of cards numbered 1 to 24. Find the odds in favor of the event.

SOLUTION

6. You choose a 10.


7. You choose an odd number.

Odds in favor =Number of unfavorable outcomesNumber of favorable outcomes

No. of odd numbers from 1 to 24 are 12

= 1212

= 1/1

SOLUTION



No. of even numbers greater than 8 between 1 to 24 are 8

Odds in favor = Number of unfavorable outcomesNumber of favorable outcomes

8. You choose an even number greater than 8.

SOLUTION

12

=

816

=


EXAMPLE 3 Finding Odds Using Probability

Basketball

Sean makes 65% of his free throws. What are Sean’s odds in favor of making a free throw?

SOLUTION

Odds

=0.650.35

Write percents as decimals.

Subtract.

0.651 – 0.65=

EXAMPLE 3

or 137

ANSWER

Sean’s odds in favor of making a free throw are 13 to 7.

Finding Odds Using Probability

Multiply by . Then simplify.100100

= 6535

,

GUIDED PRACTICE for Example 3

Odds

= 0.850.15

8515=

17or3

Subtract.

Write percents as decimals

Suppose Sean makes 85%of his free throws. What are Sean’s odds in favor of making a free throw?

9.

SOLUTION

0.851 – 0.85

=

Multiply by . Then simplify.100100

ANSWERSean’s odds in favor of making a free throw are 17 to 3.

Assignment: P. 687 #1-6, 11-20

Remember: Answers must be in simplest form (always)!

12.7 probability and odds 1

Technology