Download Lesson 4.6

Lesson 4.6 Probability of Compound Events
Vocabulary
Independent events – events that do not influence each
other.
Rule: Probability of Two Independent Events
If A and B are independent events,
P(A and B) = P(A) • P(B).
Independent Events
ALGEBRA 1 LESSON 4-6
Suppose you roll two number cubes. What is the probability
that you will roll an odd number on the first cube and a multiple of 3
on the second cube?
3
1
2
1
There are 3 odd numbers out of
six numbers.
P(odd) = 6 = 2
There are 2 multiples of 3 out of
6 numbers.
P(odd and multiple of 3) = P(odd) • P(multiple of 3)
P(multiple of 3) = 6 = 3
1
1
= 2• 3
Substitute.
= 1
Simplify.
6
The probability that you will roll an odd number on the first cube and a
multiple of 3 on the second cube is 1 .
6
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Selecting With Replacement
ALGEBRA 1 LESSON 4-6
Suppose you have 3 quarters and 5 dimes in your pocket.
You take out one coin, and then put it back. Then you take out
another coin. What is the probability that you take out a dime and then
a quarter?
Since you replace the first coin, the events
are independent.
5
P(dime) = 8
There are 5 out of 8 coins that are dimes.
3
P(quarter) = 8
There are 3 out of 8 coins that are quarters.
P(dime and quarter) = P(dime) • P(quarter)
5
3
= 8 •8
Multiply.
15
= 64
15
The probability that you take out a dime and then a quarter is 64 .
4-6
Probability of Compound Events
ALGEBRA 1 LESSON 4-6
You roll two number cubes. Find each probability.
1. P(odd and even)
1
4
2. P(1 or 2 and less than 5)
2
9
You select letters from the following: A A B B B C D D E F G G G
and replace them. Find each probability.
3. P(A then B)
1
26
4. P(vowel then G)
3
52
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