Download 2-7 - Mr Forbes EHS Math

Probability of Compound Events
Lesson 2-7
Algebra 1
Additional Examples
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
Probability of Compound Events
Lesson 2-7
Algebra 1
Additional Examples
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
3
P(quarter) = 8
There are 5 out of 8 coins that are dimes.
There are 3 out of 8 coins that are quarters.
P(dime and quarter) = P(dime) • P(quarter)
5
3
= 8 •8
15
Multiply.
= 64
15
The probability that you take out a dime and then a quarter is 64 .
Probability of Compound Events
Lesson 2-7
Algebra 1
Additional Examples
Suppose you have 3 quarters and 5 dimes in your pocket.
You take out one coin, but you do not put it back. Then you take out
another coin. What is the probability of first taking out a dime and then
a quarter?
5
P(dime) = 8
3
P(quarter after dime) = 7
There are 5 out of 8 coins that are dimes.
There are 3 out of 7 coins that are quarters.
P(dime then quarter) = P(dime) • P(quarter after dime)
5
3
= 8 •7
15
Multiply.
= 56
15
The probability that you take out a dime and then a quarter is 56 .
Probability of Compound Events
Lesson 2-7
Algebra 1
Additional Examples
A teacher must select 2 students for a conference. The
teacher randomly picks names from among 3 freshmen,
2 sophomores, 4 juniors, and 4 seniors. What is the probability that a
junior and then a senior are chosen?
4
P(junior) = 13
There are 4 juniors among 13 students.
There are 4 seniors among 12 remaining
students.
4
P(senior after junior) = 12
P(junior then senior) = P(junior) • P(senior after junior)
4
4
= 13 • 12
16
4
= 156 = 39
Substitute.
Simplify.
4
The probability that the teacher will choose a junior then a senior is 39.