1. 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
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2. 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
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3. 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
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4. 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
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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
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6. 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
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