Conditional Probability
Topic 15: Conditional Probability, Expected Value, and Strategy
in
Sports
CCLS
standards
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on two categorical
and quantitative variables.
 Summarize categorical data for two categories in two-way
frequency tables. Interpret relative frequencies in the
content of the data (including joint, marginal, and
conditional relative frequencies). Recognize possible
associations and trends in the data.
Conditional Probability and the Rules of Probability
Understand independence and conditional probability and
use them to interpret data
 Understand the conditional probability of A given B as P(A
and B)/P(B), and interpret independence of A and B as
saying that the conditional probability of A given B is the
same as the probability of A, and the conditional
probability of B given A is the same as the probability of B.
 Construct and interpret two-way frequency tables of data
when two categories are associated with each object being
classified. Use the two-way table as a sample space to
decide if events are independent and to approximate
conditional probabilities.
 Recognize and explain the concepts of conditional
probability and independence in everyday language and
everyday situations.
Use the rules of probability to compute probabilities of
compound events in a uniform probability model
 Find the conditional probability of A given B as the
fraction of B’s outcomes that also belong to A, and
interpret the answer in terms of the model.
 Apply the general Multiplication Rule in a uniform
probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B),
and interpret the answer in terms of the model.
Homework 6, 8, 10, 12, 14, 46
Conditional Probability
Conditional Probability
Name: ________________________________
Probability & Statistics
1.
Date: ____
CW/HW #71
Suppose you select an adult male at random from the United States.
Which of the following probabilities is larger, P(plays in NBA | over 6
feet tall) or P(over 6 feet tall | plays in NBA)?
Explain.
2.
Consider the outcomes of Chicago Bulls home games and whether or
not fans received a free Big Mac.
Suppose that we randomly select a Bulls home game.
a. What is the probability that the Bulls won the game, given that
fans received a free Big Mac?
b. What is the probability that fans received free Big Mac, given
that the Bulls won the game?
Conditional Probability
3.
In 2010, Jose Bautista of the Toronto Blue Jays led the Major
Leagues with 54 home runs. The table below summarizes the
outcomes of the Blue Jays’ 81 home games and whether or not
Bautista hit at least 1 home run in the game.
Suppose that we randomly select 1 Blue Jays home game in 2010.
a. What is the probability that a fan at the game saw a Blue Jays win
and a Bautista home run?
b. What is the probability that a fan at the game saw a Blue Jays win
or a Bautista home run?
c. What is the probability that a fan at the game saw a Bautista
home run, given that the Blue Jays lost the game?
d. What is the probability that a fan didn’t see a Bautista home run,
given that the Blue Jays won the game?
e. What is the probability that the Blue Jays won, given that
Bautista hit a home run?
f. What is the probability that the Blue Jays won, given that
Bautista did not hit a home run?
Conditional Probability
g. Based on your answers to (e) and (f), are the events ‘Blue Jays win’
and ‘Bautista hits a home run’ independent?
Explain.