Post on 10-Jan-2016
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Essential Question: What makes conditional probability different from normal probability?
A conditional probability contains a condition that may limit the sample space for the event. We can write a conditional probability event using the notation P(B | A), which means “the probability of event B, given event A”.
Order matters when calculating conditional probability.
We can calculate conditional probability from a table (next slide)
The table below shows the results of a class survey if students did a household chore last night. Find P(did a chore | male)
The second condition limits the sample space to only males (15 total). Of those 15, 7 did a chore, so P(did a chore | male) = 7/15
Use the table above to find P(female | did a chore)
Yes
No
Male 7 8
Female
7 6
7/14 = 1/2
YOUR TURN The table below shows recycling data
for a recent year. Find the probability that a sample of recycled waste was paper.
Find P(paper | recycled)
36.7/68 .54
Material
Recycled
Not Recycled
Paper 36.7 45.1
Metal 6.3 11.9
Glass 2.4 10.1
Plastic 1.4 24.0
Other 21.2 70.1
You can use a formula to find conditional probability
P(B | A) = P(A and B)P(A)
Example: 80% of an airline’s flights depart on schedule. 72% of its flights depart and arrive on schedule. Find the probability that a flight that departs on time also arrives on time.
.72/.80 = 0.9
YOUR TURN P(B | A) = P(A and B)
P(A) Researchers asked people who exercise
regularly whether they jog or walk. 58% of the respondents were male. 20% of all respondents were males who said they jog. Find the probability that a male respondent jogs.
.20/.58 = 0.34 (about 34%)
You can use a tree diagram to solve problems involving conditional probabilities.
A student in Buffalo, NY made the following observations: Of all snowfalls, 5% are heavy (at least 6 in) After a heavy snowfall, schools are closed 67%
of the time After a light (less than 6 in) snowfall, schools
are closed 3% of the time. Find the probability that the snowfall is light
and the schools are open (next slide)
5% are heavy snowfall After heavy, 67% chance school closed After light, 3% chance school closed Find P(light snow and schools open)
0.05
0.95
Heavy
Light
0.67
0.33
0.03
0.97
Closed
Open
Closed
Open
0.95 0.97 = 0.92
YOUR TURN Find P(schools open and heavy snow)
0.05
0.95
Heavy
Light
0.67
0.33
0.03
0.97
Closed
Open
Closed
Open
0.05 0.33 = 0.0165
ASSIGNMENT Page 656 – 657
Problems 1 – 12 (all)