13.4 Independent Events13.4 Independent Events

Student Study GuideStudent Study Guide

Tree DiagramsTree Diagrams1. 3x3=9 2. 3x4=12

3. 3x2=6 4. 3x4=121. 3x3=9 2. 3x4=12

3. 3x2=6 4. 3x4=12

How does a quiet Hawaiian laugh?How does a quiet Hawaiian laugh?1. 6^5 = 7776 2. 4x3x2=24

3. 5x4=20 4. 6x3=18

5. 12x6x4=288 6. 2^8=256

7. 5^3=125

With alowha

1. 6^5 = 7776 2. 4x3x2=24

3. 5x4=20 4. 6x3=18

5. 12x6x4=288 6. 2^8=256

7. 5^3=125

With alowha

StrawberryStrawberry

M&MsM&Ms

WalnutsWalnuts

StrawberriesStrawberries

BananaBanana

VanillaVanilla

M&MsM&Ms

WalnutsWalnuts

StrawberriesStrawberries

M&MsM&Ms

WalnutsWalnuts

StrawberriesStrawberries

3x3 = 93x3 = 9

Independent EventsIndependent Events

Two events are independent if the occurrence of one does not affect the probability of the occurrence of the other.

Two events are independent if the occurrence of one does not affect the probability of the occurrence of the other.

1. The first marble is green and the second is yellow.

1. The first marble is green and the second is yellow.

10 X 5 =

18 18

10 X 5 =

18 18

50 =

324

50 =

324

25

162

25

162

A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find the probability if the marbles are replaced.

A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find the probability if the marbles are replaced.

A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find the probability if the marbles are replaced.

A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find the probability if the marbles are replaced.

3. The first marble is red and the second is yellow.

3. The first marble is red and the second is yellow.

3 X 5 =

18 18

3 X 5 =

18 18

15 =

324

15 =

324

5

108

5

108

5. Neither marble is green.5. Neither marble is green.

8 X 8 =

18 18

8 X 8 =

18 18

64 =

324

64 =

324

16

81

16

81

A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find

the probability if the marbles are replaced.

A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find

the probability if the marbles are replaced.

A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find

the probability.

A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find

the probability.

7. The first marble is yellow and the second is red.

7. The first marble is yellow and the second is red.

5 X 3 =

18 18

5 X 3 =

18 18

15 =

324

15 =

324

5

108

5

108

Practice Masters Level BPractice Masters Level B

A red number cube and a green number cube are rolled together. Find the

probability of each event.

A red number cube and a green number cube are rolled together. Find the

probability of each event.1. The green cube is odd and the red cube

is even.1. The green cube is odd and the red cube

is even.

3 X 3 =

6 6

3 X 3 =

6 69 =

36

9 =

36

1

4

1

4

Green: 1, 3, 5Green: 1, 3, 5

Red: 2, 4, 6Red: 2, 4, 6

A red number cube and a green number cube are rolled together. Find the

probability of each event.

A red number cube and a green number cube are rolled together. Find the

probability of each event.3. The green cube is greater than 2 and the

red cube is greater than 5.3. The green cube is greater than 2 and the

red cube is greater than 5.

4 X 1 =

6 6

4 X 1 =

6 6

4 =

36

4 =

36

1

9

1

9

Green: 3, 4, 5, 6Green: 3, 4, 5, 6

Red: 6Red: 6

5. If the school bus is on time 8% of the time and you are on time 7% of the time, what is the probability that both you and

the bus will be on time?

5. If the school bus is on time 8% of the time and you are on time 7% of the time, what is the probability that both you and

the bus will be on time?

8% x 7% =8% x 7% = .0056 = .0056 =

0.56%

0.56%

7. If Perry is late for work 4% of the time and his boss is late 8% of the time, what is the probability that both will be late?

7. If Perry is late for work 4% of the time and his boss is late 8% of the time, what is the probability that both will be late?

4% x 8% =4% x 8% = .0032 = .0032 =

0.32%

0.32%

9. If the mail is on time 98% of the time and Anthony pays his bills on time, 95% of the time, what is the probability that

his bill payment will be received on time?

9. If the mail is on time 98% of the time and Anthony pays his bills on time, 95% of the time, what is the probability that

his bill payment will be received on time?

98% x 95% =98% x 95% = .931 = .931 =

93.1%

93.1%

Suppose that you draw two cards with replacement from a regular deck of 52 playing

cards. Find the probability of each event.

Suppose that you draw two cards with replacement from a regular deck of 52 playing

cards. Find the probability of each event.

10. Both cards are face cards.10. Both cards are face cards.

Clubs: Jack, Queen, KingClubs: Jack, Queen, King

Hearts: Jack, Queen, KingHearts: Jack, Queen, King

Diamonds: Jack, Queen, KingDiamonds: Jack, Queen, King

Spades: Jack, Queen, KingSpades: Jack, Queen, King

12 X 12 =

52 52

12 X 12 =

52 52

144 =

2704

144 =

2704

9

169

9

169

Suppose that you draw two cards with replacement from a regular deck of 52 playing

cards. Find the probability of each event.

Suppose that you draw two cards with replacement from a regular deck of 52 playing

cards. Find the probability of each event.

11. Both cards are number cards.11. Both cards are number cards.

36 X 36 =

52 52

36 X 36 =

52 52

1296 =

2704

1296 =

2704

81

169

81

169

Clubs: 2, 3, 4, 5, 6, 7, 8, 9, 10Clubs: 2, 3, 4, 5, 6, 7, 8, 9, 10

Hearts: 2, 3, 4, 5, 6, 7, 8, 9, 10Hearts: 2, 3, 4, 5, 6, 7, 8, 9, 10

Diamonds: 2, 3, 4, 5, 6, 7, 8, 9, 10Diamonds: 2, 3, 4, 5, 6, 7, 8, 9, 10

Spades: 2, 3, 4, 5, 6, 7, 8, 9, 10Spades: 2, 3, 4, 5, 6, 7, 8, 9, 10