Download 4 Conditional Probability - Notes

Conditional Probability
SWBAT:
Find conditional probability
Use tables and tree diagrams to determine conditional probability.
Experiment Yourself – This is a famous problem. On the original show, Let’s Make a Deal,
contestants were given a choice of 3 curtains. They chose one and the host, Monty Hall, would
show them a ZONK! that was behind one of the doors that they did not choose. They were
then given the opportunity to switch doors. What should they do and why?
Monty Hall Problem
This is called ___________________ __________________. It’s finding the probability that an
event will occur, given that another event occurred.
The probability of event B, given event A is written ___________________________.
Example 1 Finding Conditional Probability
The table shows students by gender and by type of school in 2005. You pick a student at
random.
Males*
2 year college
1866
4 year college
4324
Grad school
1349
*In thousands
A. What is P(female|graduate school)?
B. What is P(male|4 year college)?
C. What is P(2 year college|female)?
Females*
2462
5517
1954
You try.
Use the given contingency table to find the probabilities.
Activity
Male
Sports
276
Band/Silvertones
37
Neither
194
Female
178
68
213
A. What is P(female|playing sports)?
B. What is P(Band|male)?
C. What is P(Neither|female)?
Example 2 Conditional Probability in Statistics
Material
Paper
Metal
Glass
Plastic
Other
Recycled
45.2
7.2
3.2
2.1
21.7
Not Recycled
37.8
13.6
10.4
28.6
46.3
The above table represents the municipal waste collected in millions of tons. Americans recycle
increasing amounts through municipal waste collection. The table shows the collection data for
2007. What is the probability that a sample of recycled waste is paper?
You Try.
1. What is the probability that a sample of recycled waste is plastic?
2. What is the probability that a sample of not recycled waste is glass?
FORMULA – Conditional Probability
For any two events A and B with P(A) ≠ 0,
P(B|A) =
𝑷(𝑨 𝒂𝒏𝒅 𝑩)
𝑷(𝑨)
Example 3 Using the Conditional Probability Formula
A utility company asked 50 of its customers whether they pay their bills online or by mail.
What is the probability that a customer pays the bill online given that the customer is male?
Bill Payment
Male
Female
Online
12
24
By mail
8
6
What is the probability that a customer pays the bill by mail given that the customer is female?
You Try.
Researchers asked shampoo users whether they apply shampoo directly to the head, or
indirectly using a hand first.
Male
Female
Directly onto head Into Hand first
2
18
6
24
1. What is the probability that a respondent applies the shampoo directly to the head
given that the respondent is female?
2. What is the probability that a respondent applies the shampoo into the hand first given
that the respondent is male?
Example 4 Using a Tree Diagram
A school system compiled the following information from a survey it sent to people who were
juniors 10 years earlier.



85% of the students graduated from high school.
Of the students who graduated from high school, 90% are happy with their present jobs.
Of the students who did not graduate from high school, 60% are happy with their
present jobs.
What is the probability that a person from the junior class 10 years ago graduated from high
school and is happy with his or her job?
You Try.
1. What is the probability that a person from the junior class 10 years ago did not graduate
from high school and is not happy with his or her job?
2. What is the probability that a person from the junior class 10 years ago did not graduate
from high school and is happy with his or her job?