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 Male 8 5 6 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.