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# 13.4 Independent Events

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### 13.4 Independent Events

1. 1. 13.4 Independent Events Student Study Guide
2. 2. Tree Diagrams 1. 3x3=9 2. 3x4=12 3. 3x2=6 4. 3x4=12 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
3. 3. Strawberry M&Ms Walnuts Strawberries Banana Vanilla M&Ms Walnuts Strawberries M&Ms Walnuts Strawberries 3x3 = 9
4. 4. Independent Events <ul><li>Two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. </li></ul>
5. 5. <ul><li>1. The first marble is green and the second is yellow. </li></ul>10 X 5 = 18 18 50 = 324 25 162 A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find the probability if the marbles are replaced.
6. 6. A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find the probability if the marbles are replaced. <ul><li>3. The first marble is red and the second is yellow. </li></ul>3 X 5 = 18 18 15 = 324 5 108
7. 7. <ul><li>5. Neither marble is green. </li></ul>A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find the probability if the marbles are replaced. 8 X 8 = 18 18 64 = 324 16 81
8. 8. A bag contains 10 green marbles, 5 yellow marbles, and 3 red marbles. Find the probability. <ul><li>7. The first marble is yellow and the second is red. </li></ul>5 X 3 = 18 18 15 = 324 5 108
9. 9. Practice Masters Level B
10. 10. A red number cube and a green number cube are rolled together. Find the probability of each event. <ul><li>1. The green cube is odd and the red cube is even. </li></ul>3 X 3 = 6 6 9 = 36 1 4 Green: 1, 3, 5 Red: 2, 4, 6
11. 11. A red number cube and a green number cube are rolled together. Find the probability of each event. <ul><li>3. The green cube is greater than 2 and the red cube is greater than 5. </li></ul>4 X 1 = 6 6 4 = 36 1 9 Green: 3, 4, 5, 6 Red: 6
12. 12. 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% = .0056 = 0.56%
13. 13. 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% = .0032 = 0.32%
14. 14. 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% = .931 = 93.1%
15. 15. Suppose that you draw two cards with replacement from a regular deck of 52 playing cards. Find the probability of each event. <ul><li>10. Both cards are face cards. </li></ul>Clubs: Jack, Queen, King Hearts: Jack, Queen, King Diamonds: Jack, Queen, King Spades: Jack, Queen, King 12 X 12 = 52 52 144 = 2704 9 169
16. 16. Suppose that you draw two cards with replacement from a regular deck of 52 playing cards. Find the probability of each event. <ul><li>11. Both cards are number cards. </li></ul>36 X 36 = 52 52 1296 = 2704 81 169 Clubs: 2, 3, 4, 5, 6, 7, 8, 9, 10 Hearts: 2, 3, 4, 5, 6, 7, 8, 9, 10 Diamonds: 2, 3, 4, 5, 6, 7, 8, 9, 10 Spades: 2, 3, 4, 5, 6, 7, 8, 9, 10