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Conditional Probability.ppt
Algebra 2
Conditional Probability
Lesson 12-2
The table shows the results of a class survey.
Find P(own a pet | female)
The condition female limits the sample space to 14 possible
outcomes.
Of the 14 females, 8 own a pet.
Additional Examples
Therefore, P(own a pet | female) equals .
8
14
yesno
female86
male57
Do you own a pet?
Algebra 2
Conditional Probability
Lesson 12-2
Additional Examples
Using the data in the table, find the probability that a sample
of non-recycled waste was plastic.
The given condition limits the
sample space to non-recycled
waste.
The probability that the non-recycled waste was plastic is about
15%.
A favorable outcome is
non-recycled plastic.
MaterialRecycledNon-Recycled
Paper36.745.1
Metal6.311.9
Glass2.410.1
Plastic1.424.0
Other21.270.1
0.15
P(plastic | non-recycled) =
24.0
45.1 + 11.9 + 10.1 + 24.0 + 70.1
=
24.0
161.2
Algebra 2
Conditional Probability
Lesson 12-2
Researchers asked people who exercise regularly whether they jog
or walk. Fifty-eight percent of the respondents were male. Twenty
percent of all respondents were males who said they jog. Find the
probability that a respondent jogs given they are male.
The probability that a respondent is a male given that he jogs
is about 34%.
Additional Examples
Relate:P( male ) = 58%
P( male and jogs ) = 20%
Define:Let A = male.
Let B = jogs.
P( A and B )
P( A )
Write:P( B | A ) =
= Substitute 0.2 for P(A and B) and 0.58 for P(A).
0.344Simplify.
0.2
0.58
Algebra 2
Conditional Probability
Lesson 12-2
Additional Examples
A student made the following observations of the weather in his
hometown.
Use a tree diagram to find the probability that a day will start
out clear, and then it will rain.
P(rain|clear)= 0.28(.04) = 0.0112 ≈ 1.1%
During the mostly clear days, it rained 4% of the time.
On 28% of the days, the sky was mostly clear.
During the cloudy days it rained 31% of the time.
Algebra 2
Conditional Probability
Lesson 12-2
(continued)
b. Find the probability that it will
not rain on any given day.
The paths containing clear and no rain and cloudy and no rain
both represent
a day when it will not rain. Find the probability for both paths
and add them.
P(clear and no rain) + P(cloudy and no rain) =
P(clear) • P(no rain | clear) + P(cloudy) • P(no rain |
cloudy)
= 0.28(.96) + .72(.69)
= 0.7656
The probability that it will not rain on any given day is about
77%.
Additional Examples
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