Mutually Exclusive Events Two events A and B

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 A and B B

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

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: 1 a) Roll an even on the die 1 b) Roll an odd number on the die 2 a) Roll an odd number on a die 2 b) Roll an number greater than 3 on a die 4 a) Select a face card 4 b) Select a heart

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

Other ways to portray data Keep looking to see if Mutually Exclusive • Look at problem 31 on page 82 – What is the probability of selecting a person between 5 and 13 years old? – What is the probability of selecting a person between 25 and 44 years old? • Look at problem 32 on page 82 – What is the probability of selecting a person between 40 and 70 years old?

Other ways to portray data Keep looking to see if Mutually Exclusive • Look at the table on page 77. – What is the probability of selecting a student that earned between $100 and $299? – What is the probability of NOT selecting a student that earned between $300 and $399?

Other ways to portray data Keep looking to see if Mutually Exclusive • Look at the table on page 127 – What is the probability of the blood being type B or AB? – What is the probability of the blood being type AB or Positive? – 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?

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.