Special Topics

 Last time, we learned the Addition Rule for Mutually
Exclusive events (Disjoint Events). This was:
 P(A or B) = P(A) + P(B). This is used when events A and B can’t happen at the same time, such as getting a head or a tail on a single coin flip. You can’t get both a head and a tail on the same coin flip!
 There are other events which can happen at the same time, such as being a senior and being a student in
Special Topics.

 Let’s let event A be the event that a person is a senior.
Let’s call P(A) = .25
 Let’s let event B be the event that a person is in Special
Topics. Let’s call P(B) = .8
 Let’s also call P(A and B) = .10
 If we go by the Addition Rule for Disjoint Events, then
P(A 0r B) = .25+.8 = 1.05 ( what is wrong with this?) .
 The problem here is that a person can be both a senior and a Special Topics student at the same time. When this happens, things get counted twice !

 This is the situation in a Venn Diagram:
 Notice the intersection gets counted twice! We need a formula that corrects for this.

 Here is the formula for the General Addition Rule:
 P(A or B) = P(A) + P(B) – P(A and B). We subtract one version of the joint probability since it gets counted twice.
 When event are disjoint, the P(A and B) part of the formula equals 0. That takes us back to the formula for disjoint events: P(A or B) = P(A) + P(B).

 Musical styles other than rock and pop are becoming more popular. A survey of college students finds that the probability they like country music is .40. The probability that they liked jazz is .30 and that they liked both is .10.
What is the probability that they like country or jazz? ( Hint : a joint probability is given, so the
General Addition Rule Applies!)
 P(C or J) = .4 + .3 -.1 = .6

 What do we do to calculate the probability of two (or more) independent events happening at the same time?
 We use the Multiplication Rule for Independent
Events. The key word is the word “ and ”.
 The formula is: P(A and B) = P(A)P(B)
 What is the probability of flipping a coin and getting a head, and rolling a die and getting a six?
1 1 1
2 6 12

 Definition: Two events are independent when knowing that one occurred does not change the probability that the other occurred.
 Coin flips and dice rolls are independent.

 Section 8.1 Part 2 worksheet.