Learning Objectives
1. Compute conditional probabilities
2. Compute probabilities using the General Multiplication Rule
Conditional Probability
“Conditional Probability” is the probability that the event F occurs given that event E has occurred.
is represented as P(F|E)
EXAMPLE An Introduction to Conditional Probability
Suppose that a single six-sided die is rolled.
What is the probability that the die comes up 4?
Now suppose that the die is rolled a second time, but we are told the outcome will be an even number. What is the probability that the die comes up 4?
Conditional Probability Rule
P(F|E) can be found in one of two ways:
by dividing the probability of E and F by the probability of E
by dividing the number of outcomes in E and F by the number of outcomes in E.
EXAMPLE Conditional Probabilities on Belief about God and Region of the Country
A survey was conducted by the Gallup Organization conducted May 8 − 11, 2008 in which 1,017 adult Americans were asked, “Which of the following statements comes closest to your belief about God – you believe in God, you don’t believe in God, but you do believe in a universal spirit or higher power, or you don’t believe in either?” The results of the survey, by region of the country, are given in the table below:
Believe in God | Believe in universal spirit | Don’t believe in either | |
East | 204 | 36 | 15 |
Midwest | 212 | 29 | 13 |
South | 219 | 26 | 9 |
West | 152 | 76 | 26 |
(a) What is the probability that a randomly selected adult American who lives in the East believes in God?
(b) What is the probability that a randomly selected adult American who believes in God lives in the East?
EXAMPLE Murder Victims
In 2005, 19.1% of all murder victims were between the ages of 20 and 24 years old. Also in 2005, 16.6% of all murder victims were 20 − 24 year old males.
What is the probability that a randomly selected murder victim in 2005 was male given that the victim is 20 − 24 years old?
The General Multiplication Rule
the probability of E and F is the probability of event E occurring times the probability of event F occurring, given the occurrence of event E.
EXAMPLE General Multiplication Rule
In 2005, 19.1% of all murder victims were between the ages of 20 and 24 years old. Also in 2005, 86.9% of murder victims were male given that the victim was 20 − 24 years old.
What is the probability that a randomly selected murder victim in 2005 was a 20 − 24 year old male?