Probability Rules and Compound Events

4.2 Compound Events *Probability of A OR B*

Let’s collect data about the class: Boys Girls 9th 10th 11th 12th

a) P(Girl) = b) P(10th) = c) P(9th) = d) P(9th or 10th) =

I. Mutually Exclusive Events Notice that P(9th or 10th) = P(9 th ) + P(10 th ) Event 1: being a 9th grader Event 2: being a 10th grader

This is always true when your events are mutually exclusive. Mutually Exclusive Events: +Can’t happen at the same time +No overlap Event A: + P(A OR B) = P(A) + P(B) Boy Event B: Girl

ME or NO: Draw one card are these events mutually exclusive or not? Event 1 Event 2 ME or NO King Ace ME 2 Diamond NO Face Card Club NO Red Card Spade ME

Created By: J & J Productions II. Non Mutually Exclusive Events

If you are a girl OR a 9th grader stand up. Total Standing = ______P(Girl or 9th) = Are these events mutually exclusive? NO IS P(Girl OR 9th) = P(Girl) + P(9th)?? NO

Use your table add the number of 9th graders and the number of girls: ______What is the difference between this number and the number of people standing? ______Who is responsible for this difference? Freshmen girls

9th 10th 11th 12th TOTAL Boy Girls TOTALS

For events that are NOT Mutually Exclusive: You must subtract the overlap! P(A or B) = P(A) + P(B) – overlap P(A or B) = P(A) + P(B) – P(A AND B)

9th Girl 9th Girls

Draw one card are these events mutually exclusive or not? Event Event P(A) P(B) P(A OR B)

Created By: J & J Productions A B King Ace 4/52 = 1/13 4/52 = 1/13 2/13 2 Club 4/52 13/52 17/52 – 1/52 = 16/52 = 4/13 Face Club 16/52 13/52 29/52 – 4/52 =25/52 Red Spade 26/52 13/52 39/52

EXAMPLES

1. You roll a die. What is the probability that you get an even number? P(2 OR 4 OR 6) These Events ARE mutually exclusive P(2) + P(4) + P(6) 1/6 + 1/6 + 1/6 = 3/6 = 0.5

2. You are eating M&M’s. Your bag contents are represented by the following table:

Brown Yellow Red Orange Green Blue TOTAL 5 15 10 2 8 10 50

If you select a candy from the bag at random, what is P(Green OR Blue)??

These events ARE mutually exclusive!! P(Green) + P(Blue) = 8/50 + 10/50 = 18/50 = 0.36

3. Mr. Orr has asked the Math and English departments to pinpoint students in the sophomore class who need additional

Created By: J & J Productions help in these subjects to prepare for the ACT. The data compiled shows that 80% of the students need help in Math, 70% need help in English, and 55% need help in both subjects.

a.) Use the appropriate formula to compute the probability a student would need Math or need English. not mutually exclusive – P(nM) +P(nE) – P(nM and nE) 0.80 + 0.70 – 0.55 = 0.95

2.) At the University of Kentucky, a random selection of 140 people was asked what political party they associated themselves with. The people were grouped into two categories, students or professors. For notation purposes, we will use S(student), P(professor), D(democrat), R(republican), I(independent). Suppose a person was selected at random out of the 140, find the following probabilities:

Person Democrat Republican Independent Row Total Type (D) (R) (I) Professor 5 34 9 48 Student 63 21 8 92 Column 68 55 17 140 *Grand Total Total

a) Compute P(D or P)  Are these mutually exclusive? NO – some professors are democrats P(D or P) = P(D) + P(P) – P(D and P) 68 48 5 111 P(D or P) =     0.793 140 140 140 140

Created By: J & J Productions