Transcript (12-5)Probablilty

COURSE 2 LESSON 12-5
Compound Events
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?
1
1
Since 3 of the marbles are blue, the probability of drawing a blue marble is 3 .
P(blue, then blue) = P(blue)  P(blue)
1
= 3

1
3
Selecting blue is the first
and second event.
Substitute.
1
= 9
Multiply.
1
The probability that both marbles will be blue is 9 .
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COURSE 2 LESSON 12-5
Compound Events
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)
1
= 10

1
= 100
1
10
Selecting 2 is the first event.
Selecting 5 is the second event.
Substitute.
Multiply.
The probability that you will spin a 2 and a 5 is
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1
.
100
COURSE 2 LESSON 12-5
Compound Events
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.
2
P(not vowel) = 6
1
P(not vowel) = 3
number of cards not a vowel
number of cards remaining
Simplify.
The probability of selecting a non-vowel for the second card is
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1
.
3
COURSE 2 LESSON 12-5
Compound Events
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)
3
= 8

4
7
Substitute.
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Use the formula for
dependent events.
COURSE 2 LESSON 12-5
Compound Events
(continued)
12
= 56
Multiply.
3
= 14
Simplify.
3
The probability that the two marbles are red and white is 14 .
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COURSE 2 LESSON 12-5
Compound Events
Find each probability.
1. You roll a number cube twice. What is P(2 and even)?
1
12
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
90
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