1. You choose an O. 2. You choose an M.

You choose a card at random from a bag which contains cards with the letters in the word MONOPOLY. Find the probability.

Lesson 12.8, For use with pages 694-700

1. You choose an O. 2. You choose an M.

You choose a card at random from a bag which contains cards with the letters in the word MONOPOLY. Find the probability.

ANSWER 38

Lesson 12.8, For use with pages 694-700

ANSWER 18

Dependent & Independent Events

Section 12. 8

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?

• Events that contain more than one outcome are called compound events.

• Sometime the occurrence of one event affects the probability of the second event, and sometimes it has no effect.

• If there is no effect, we say the events are independent events.

• Dependent events – events for which the occurrence of one AFFECTS the probability of the other.

• If events A and B are independent events, then the probability of A and B occurring is given by P(A & B) = P(A) x P(B)

• This is the Multiplication Property for compound events

Independent or Dependent?• A number cube is rolled twice.• It is raining outside and the parade is canceled.

• The first roll of a number cube is 4, and the sum of the first two rolls is 5.

• It is sunny and a movie theater changes its movie.

• Two cards are drawn, one after the other, from a deck of cards. The first card drawn is not replaced.

• Joey got an A on his math test so he will get an A on his science test.

Independent

Dependent

Dependent

Independent

Dependent

Independent

GUIDED PRACTICE for Examples 1and 2

In Exercises 1 and 2, tell whether the events are independent or dependent. Explain your reasoning.

1. You toss a coin. Then you roll a number cube.

You randomly choose 1 of 10 marbles. Then you randomly choose one of the remaining 9 marbles.

2.

The coins toss does not affect the roll of a dice, so the events are independent.

ANSWER

There is one fewer number in the bag for the second draw, so the events are dependent.

ANSWER

5 blue

6 yellow

11 red

8 green

30 total

1. Probability of yellow, yellow with replacement

2. Probability of yellow, yellow without replacement

3. Probability of red, blue with replacement

4. Probability of red, blue without replacement

5. Probability of green, yellow with replacement

6. Probability of green, yellow without replacement

EXAMPLE 2 Standardized Test Practice

The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss resulting in a win.

So the probability of each event is .125

ANSWER

The probability of two winning tosses in a row is .625

1

The correct answer is A.

P (win and win) = P (win) P (win)251 1

25 =

GUIDED PRACTICE for Examples 1and 2

3. You toss a coin twice. Find the probability of getting two heads.

P(head and head) = P(head) P(head)

= 14

or 25%

12

12=

The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss

ANSWER

Daily Homework Quiz

For use after Lesson 12. 8

2. A bag contains ten cards numbered 1 through 10. You pick one card and then another without replacement. What is the probability that both cards display a value of 6 or higher?

ANSWER 2 9

–, 0.25/10 x 4/9

Daily Homework Quiz

For use after Lesson 12. 8

1. Events A and B are independent. P(A & B) = P(A) x P(B)

P(A) 0.75, P(B) 0.5 , P(A and B) _____

ANSWER 0.75 x 0.5 = 0.375

Daily Homework Quiz

For use after Lesson 12. 8

1. Events A and B are dependent. P(A & B) = P(A) x P(B)

P(A) 0.75, P(B given A) _?_ , P(A and B) 0.3

ANSWER 0.3 ÷ 0.75 = 0.4

Homework

• Page 697 #1-9, 17-20, 23-26