Compound Events COURSE 2 LESSON 12-5

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Presentation transcript:

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? Since of the marbles are blue, the probability of drawing a blue marble is . 1 3 P(blue, then blue) = P(blue)  P(blue) Selecting blue is the first and second event. Substitute. =  1 3 Multiply. = 1 9 The probability that both marbles will be blue is . 1 9 12-5

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. P(2 and 5) = P(2)  P(5) Selecting 2 is the first event. Selecting 5 is the second event. Substitute. =  1 10 Multiply. = 1 100 The probability that you will spin a 2 and a 5 is . 1 100 12-5

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. P(not vowel) = 2 6 number of cards not a vowel number of cards remaining Simplify. 1 3 P(not vowel) = The probability of selecting a non-vowel for the second card is . 1 3 12-5

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. P(red, then white) = P(red)  P(white after red) Use the formula for dependent events. Substitute. =  3 8 4 7 12-5

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

Compound Events Find each probability. 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)? 1 12 1 90 12-5