Download 12-2 Conditional Probability

12-2 Conditional Probability
Hubarth
Algebra II
Conditional probability contain a condition that may limit the sample space for an event. You
can write a conditional probability using the notation P(B|A), read “ the probability of event B,
given event A.”
Ex. 1 Finding Conditional Probability
The table shows the results of a class survey.
Find P(own a pet | female)
Do you own a pet?
yes
no
female 8
6
male
5
7
The condition female limits the sample space to 14 possible outcomes.
Of the 14 females, 8 own a pet.
Therefore, P(own a pet | female) equals 8 .
14
Ex. 2 Real-World Connection
Using the data in the table, find the probability that a sample of nonrecycled waste was plastic.
Material
Recycled
Paper
36.7
Metal
6.3
Glass
2.4
The given condition limits the
Plastic
1.4
sample space to non-recycled
Other
21.2
waste.
Non-Recycled
45.1
11.9
10.1
24.0
70.1
A favorable outcome is
non-recycled plastic.
P(plastic | non-recycled) =
=
24.0
45.1 + 11.9 + 10.1 + 24.0 + 70.1
24.0
161.2
0.15
The probability that the non-recycled waste was plastic is about 15%.
Ex. 3 Real-World Connection
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 male respondent jogs.
Relate: P( male ) = 58%
P( male and jogs ) = 20%
Define: Let A = male.
Let B = jogs.
Write:
P( A | B ) =
=
P( A and B )
P( A )
0.2
0.58
Substitute 0.2 for P(A and B) and 0.58 for P(A).
0.344
Simplify.
The probability that a male respondent jogs is about 34%.
Ex. 4 Making a Tree Diagram
A student made the following observations of
the weather in his hometown.
• On 28% of the days, the sky was mostly clear.
• During the mostly clear days, it rained 4% of the time.
• During the cloudy days it rained 31% of the time.
Use a tree diagram to find the probability that a day will
start out clear, and then it will rain.
The path containing clear and rain represent days that start out clear and then
will rain.
P(clear and rain) = P(rain | clear) • P(clear)
= 0.04 • 0.28
= 0.011
The probability that a day will start out clear and then rain is about 1%.
Practice
1. Use the table to find P(female| do not own a pet)
female
male
6
3
=
14 7
2. Find the probability that a sample of non-recylced waste was paper.
45.1
161.2
yes
8
5
no
6
7
= 0.2797 or 28%
3. Eighty percent of an airline’s flights depart on schedule. Seventy-two percent of its flights
depart and arrive on schedule. Find the probability that a flight that departs on time also
arrives on time.
.72
= .9
.8
4. Find the probability that the day will start off cloudy and then
will rain.
𝑃 𝑟𝑎𝑖𝑛 𝑐𝑙𝑜𝑢𝑑𝑦 ∙ 𝑃 𝑐𝑙𝑜𝑢𝑑𝑦 = .31 ∙ .72
= .22