13.4 independent events
TRANSCRIPT
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