http://www.ck12.org Chapter 2. Conditional Probability
- Donna discusses with her parents the idea that she should get an allowance. She says that in her class, 55%
of her classmates receive an allowance for doing chores, and 25% get an allowance for doing chores and are
good to their parents. Her mom asks Donna what the probability is that a classmate will be good to his or her
parents given that he or she receives an allowance for doing chores. What should Donna’s answer be? - At a local high school, the probability that a student speaks English and French is 15%. The probability that
a student speaks French is 45%. What is the probability that a student speaks English, given that the student
speaks French? - At a local high school, the probability that a student takes statistics and art is 10%. The probability that a
student takes art is 65%. What is the probability that a student takes statistics, given that the student takes art? - The test for a disease is accurate 80% of the time, and 2.5% of the population has the disease. What is the
probability that you have the disease, given that you tested positive? - For question 9, what is the probability that you don’t have the disease, given that you tested negative?
Summary
This chapter begins with learning how to draw and use tree diagrams as a way to visualize and calculate probabilities.
It then moves on to the more complex caculations of permuations and combinations - where permutations are events
where the order matters, and combinations are events where the order doesnotmatter. Givenntotal number of
objects, androbjects chosen is expressed asnPr, the number ofpermutations(with order) is:
nPr=n!
(n−r)!while the number ofcombinations(without order) is:
nCr=n!
r!(n−r)!The chapter concludes with how to calculate using conditional probability, where a second event depends on the first
event.