Transcript conditional probability

Conditional Probability
Finding Conditional Probability
 Definition 1: A conditional probability contains 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.”
Example 1
 The table shows the results of a class survey.
 A. Find P(did a chore | male).
 B. Find P(female | did a chore).
Example 2
 Recycle Americans recycle increasingly more materials through municipal
waste collection each year. The table shows recycling data for a recent year. Find
the probability that a sample of recycled waste was paper.
 Find the probability that a sample of recycled waste was paper.
 Find the probability that a sample of recycled waste was plastic.
Using Formulas and Tree Diagrams
 Property: Conditional Probability Formula:
 For any two events A and B from a sample space with
P(A) ≠ 0.
Example 3
 Market Research Researchers asked shampoo users
whether they apply shampoo directly to the head, or
indirectly using a hand. Find the probability that a
respondent applies shampoo directly to the head,
given that the respondent is female.
P(directly to head|female) =
Ticket Out the Door
 The table below shows the results of a class survey.
Do You Own a Pet?
Yes
No
Female
8
6
Male
5
7
1. Find P(own a pet|female).
2. Find P(male|don’t own a pet).
Tree Diagrams
Example 4
 A student in Buffalo, New York, made the observations
below.
 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.
 Make a tree diagram. Use H for heavy snowfall, L for light
snowfall, C for schools closed, and O for schools open.
Example 4 Continued
 a. Find P(L and O)
 b. Find P(Schools open, given heavy snow)
Example 5
 Make a tree diagram based on the survey results below.
Then find P(a female respondent is left-handed) and P(a
respondent is both male and right-handed).
 Of all the respondents, 17% are male.
 Of the male respondents, 33% are left-handed.
 Of female respondents, 90% are right-handed.
 P(female is left-handed) =
 P(both male and right-handed) =
Ticket Out the Door
 A student made the following observations of the
weather in his hometown.
 On 28% of the days, the sky is 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.