Mutually Exclusive Events Two events A and B are mutually exclusive if A and B cannot occur at the same time Mutually Exclusive Not Mutually Exclusive A B A B A and B

Are the Events Mutually Exclusive? Draw the sample space 1a) Roll an even on the die, or 1b) Roll an odd number on the die 2a) Roll an odd number on a die, or 2b) Roll an number greater than 3 on a die 3a) Select a male student, or 3b) Select a student over 5’ 10” 4a) Select a face card, or 4b) Select a heart

P(A or B) = P(A) + P(B) – P(A and B) The Addition Rule The probability that events A or B will occur, P(A or B), is given by: P(A or B) = P(A) + P(B) – P(A and B) If events A and B are mutually excusive, then the rule can be simplified to: P(A or B) = P(A) + P(B) This rule can be extended to any number of events.

Are the Events are Mutually Exclusive? Calculate the probability of: 1a) Roll an even on the die, or 1b) Roll an odd number on the die 2a) Roll an odd number on a die, or 2b) Roll a number greater than 3 on a die 3a) Select a face card, or 3b) Select a heart

Are the Events are Mutually Exclusive Are the Events are Mutually Exclusive? Draw the sample space Calculate the Probability 1a) Roll less than 3 on the die, or 1b) Roll greater than 4 on the die 2a) Roll less than 5 on a die, or 2b) Roll greater than 2 on a die 3a) Roll less than 5 on a die, or 3b) Roll an even number on a die 4a) Select an even numbered card, or 4b) Select a heart

Mutually Exclusive Events Example 1: Find the probability that a girl’s favorite department store is Macy’s or Nordstrom. Find the probability that a girl’s favorite store is not JC Penny’s. 0.45 0.90 Macy’s 0.25 Saks 0.20 Nordstrom JC Pennys 0.10 Bloomingdale’s

Mutually Exclusive Events Example 2: When rolling two dice, what is probability that your sum will be 4 or 5? 7/36

Mutually Exclusive Events Example 3: What is the probability of picking a queen or an ace from a deck of cards 2/13

P(A or B) = P(A) + P(B) - P(AB) Overlapping Events Probability that non-mutually exclusive events A and B or both will occur expressed as: P(A or B) = P(A) + P(B) - P(AB)

Overlapping Events Example 1: Find the probability of picking a king or a club in a deck of cards.

Overlapping Events Fem Male FL 8 4 AL 6 3 GA 7 Example 2: Find the probability of picking a female or a person from Florida out of the committee members. Fem Male FL 8 4 AL 6 3 GA 7

Overlapping Events Example 3: When rolling 2 dice, what is the probability of getting an even sum or a number greater than 10?

Other ways to portray data Keep looking to see if Mutually Exclusive Japan’s estimated population for the year 2010 is given in the following bar graph. What is the probability of a person selected at random being between the ages of 20 and 40 years of age?

Other ways to portray data Keep looking to see if Mutually Exclusive (12.2 + 14 + 18.3) / 127.1 = 44.5 / 127.1 = 0.35

Average Monthly Earnings of College Students What is the probability of selecting a student that earned between $300 and $399? What is the probability selecting a student that earned between $100 and $299? 0.12 0.23

Average Monthly Earnings of College Students What is the probability selecting a student that had a job? What is the probability of NOT selecting a student that earned between $400 and $499? 1 - 0.33 = .67 1 – 0.11 = 0.89

Other ways to portray data Keep looking to see if Mutually Exclusive Blood Type O A B AB Total RH Factor Positive 156 139 37 12 344 Negative 28 25 8 4 65 184 164 45 16 409 What is the probability of the blood being type B or AB? What is the probability of the blood being type AB or Positive? (45 + 16)/409 = 61/409 = 0.15 (16 + 344 – 12) / 409 = 348 / 409 = 0.85

Other ways to portray data Keep looking to see if Mutually Exclusive Blood Type O A B AB Total RH Factor Positive 156 139 37 12 344 Negative 28 25 8 4 65 184 164 45 16 409 What is the probability of the blood being type A or B or Negative? What is the probability of the blood NOT being type O or negative? (164 + 45 + 65 – 25 – 8) / 409 = 241 / 409 = 0.589 1 – (184 + 65 – 28) / 409 = 1 – 221 / 409 = 1 – 0.54 = 0.46

Venn Diagrams The probability of me buying a car this weekend is .43. The probability of my wife bringing a cat home this weekend is 0.60. The probability of me buying a car and she bringing a cat home is 0.23. Find the probability of neither of us bringing something home.

Venn Diagrams The probability of: Me getting a dog is .35 My wife getting a cat 0.50. My daughter getting a cat is 0.45 Me and my wife getting our pet is 0.15 Me and my daughter getting our pet is 0.10 My wife and daughter getting their per is 0.25 All of us getting pets is 0.1 Find the probability of none of us getting a pet.

Class Work pg 353, # 1 – 4, and Handout: 5-41 through 5-51 all