Determine whether the events are or Then find the probability. Round to mutually exclusive not mutually exclusive. the nearest hundredth. 1. SHELTER selecting a cat or dog at the animal shelter that has 15 cats, 25 dogs, 9 rabbits and 3 horses 2. GAME rolling a 6 or an even number on a die while playing a game 3. AWARDS The student of the month gets to choose his or her award from 9 gift certificates to area restaurants, 8 CDs, 6 DVDs, or 5 gift cards to the mall. What is the probability that the student of the month chooses a CD or DVD? 4. STUDENT COUNCIL According to the table shown at the committee Soph. junior senior right, what is the probability that a person on a student service 4 5 6 council committee is a junior or on the service committee? Advertising 3 2 2 Dances 4 8 6 13-6 Study Guide and Administrative 1 1 4 Liaison Intervention (continued) Probabilities of Mutually Exclusive Events Probabilities of Complements The complement of an event is all of the outcomes in the sample space that are not A included as outcomes of event A. Probability of the Complement P(not A) = 1 P(A) – of an Event Example: A school has a photography display of 100 pictures. One of the pictures will be chosen for display at the district office. Lorenzo has 3 pictures on display. What is the probability that one of his photographs is not chosen? Let represent selecting one of Lorenzo’s photographs. A Then find the probability of the complement of A. = 1 P(not A) P(A) – Probability of a complement = 1 − Substitution = or 0.97 Simplify The probability that one of Lorenzo’s photos is not selected is 97%. Exercises Determine the probability of each event. 1. If there is a 4 in 5 chance that your mom will tell you to clean your room today after school, what is the probability that she won’t?
Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. Round to the nearest hundredth. 1. SHELTER selecting a cat or dog at the animal shelter that has 15 cats, 25 dogs, 9 rabbits and 3 horses 2. GAME rolling a 6 or an even number on a die while playing a game 3. AWARDS The student of the month gets to choose his or her award from 9 gift certificates to area restaurants, 8 CDs, 6 DVDs, or 5 gift cards to the mall. What is the probability that the student of the month chooses a CD or DVD? committee Soph. junior senior service 4 5 6 Advertising 3 2 2 Dances 4 8 6 Administrative Liaison 1 1 4 4. STUDENT COUNCIL According to the table shown at the right, what is the probability that a person on a student council committee is a junior or on the service committee? 13-6 Study Guide and Intervention (continued) Probabilities of Mutually Exclusive Events Probabilities of Complements The complement of an event A is all of the outcomes in the sample space that are not included as outcomes of event A. Probability of the Complement of an Event P(not A) = 1 – P(A) Example: A school has a photography display of 100 pictures. One of the pictures will be chosen for display at the district office. Lorenzo has 3 pictures on display. What is the probability that one of his photographs is not chosen? Let A represent selecting one of Lorenzo’s photographs. Then find the probability of the complement of A. P(not A) = 1 – P(A) Probability of a complement = 1 − Substitution = or 0.97 Simplify The probability that one of Lorenzo’s photos is not selected is 97%. Exercises Determine the probability of each event. 1. If there is a 4 in 5 chance that your mom will tell you to clean your room today after school, what is the probability that she won’t?
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