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Compound Events

1 3. 1 3. Since of the marbles are blue, the probability of drawing a blue marble is. Selecting blue is the first and second event. P (blue, then blue) = P (blue)  P (blue). Substitute. 1 3. 1 3. = . 1 9. =. Multiply. 1 9.

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Compound Events

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  1. 1 3 1 3 Since of the marbles are blue, the probability of drawing a blue marble is . Selecting blue is the first and second event. P(blue, then blue) = P(blue)P(blue) Substitute. 1 3 1 3 =  1 9 = Multiply. 1 9 The probability that both marbles will be blue is . Compound Events COURSE 2 LESSON 12-5 A box contains the same number of green marbles, orange marbles, and blue marbles. You draw one marble, replace it, and draw a second marble. What is the probability that both marbles you draw are blue? 12-5

  2. Selecting 2 is the first event. Selecting 5 is the second event. P(2 and 5) = P(2)P(5) =  Substitute. 1 10 1 10 = Multiply. 1 100 1 100 The probability that you will spin a 2 and a 5 is . Compound Events COURSE 2 LESSON 12-5 A spinner has equal sections labeled 1–10. Suppose you spin twice. Find P(2 and 5). The two events are independent. There are 10 possibilities on each spin. 12-5

  3. number of cards not a vowel P(not vowel) = number of cards remaining 2 6 1 3 P(not vowel) = Simplify. 1 3 The probability of selecting a non-vowel for the second card is . Compound Events COURSE 2 LESSON 12-5 You select a card at random from those having A, E, I, O, U, P, C. The card has the letter E. Without replacing the E card, you select a second card. Find the probability of selecting a card that does not have a vowel. There are 6 cards remaining after selecting an E card. 12-5

  4. Use the formula for dependent events. P(red, then white) = P(red)P(white after red) 3 8 4 7 =  Substitute. Compound Events COURSE 2 LESSON 12-5 A bag contains 3 red marbles, 4 white marbles, and 1 blue marble. You draw one marble. Without replacing it, you draw a second marble. What is the probability that the two marbles you draw are red and white? The two events are dependent. After the first selection, there are 7 marbles to choose from. 12-5

  5. 12 56 = Multiply. Simplify. = The probability that the two marbles are red and white is . 3 14 3 14 Compound Events COURSE 2 LESSON 12-5 (continued) 12-5

  6. 1 12 1 90 Compound Events COURSE 2 LESSON 12-5 Find each probability. 1. You roll a number cube twice. What is P(2 and even)? 2. You draw a card at random from a stack of ten cards, each labeled with a number from 1 through 10. Then you draw a second card. What is P(5, then 3)? 12-5

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