Chapter 10 – Data Analysis and Probability 10.7 – Probability of Compound Events

Compound Event – When two or more events occur together Union of Events – all of the outcomes that are in either A or B. Intersection of Events – all of the outcomes shared by both A and B.

10.7 – Probability of Compound Events Overlapping events – two events that have outcomes in common Mutually Exclusive (Disjoint) Events – two events that have no outcomes

10.7 – Probability of Compound Events Probability of Compound Events Overlapping Events – If A and B are overlapping events, then P(A and B) ≠ 0 The probability of A or B is P(A or B) = P(A) + P(B) – P(A and B) Mutually Exclusive Events – If A and B are disjoint events, then P(A and B) = 0 The probability of A or B is P(A or B) = P(A) + P(B)

10.7 – Probability of Compound Events Example 1 A six-sided die is rolled. What is the probability that the number rolled is less than 3 or greater then 5?

10.7 – Probability of Compound Events Example 2 A six-sided die is rolled. What is the probability of rolling a number greater than 4 or even?

10.7 – Probability of Compound Events Example 3 Of 100 students surveyed, 92 own either a car or a computer. Also, 65 own cars and 82 own computers. What is the probability that a randomly selected student owns both a car and a computer?

10.7 – Probability of Compound Events Complement of an Event – all outcomes that are not in the event. Probability of the Complement of an Event – The sum of the probabilities of an event and its complement is 1. P(A) + P(not A) = 1, so P(not A) = 1 – P(A)

10.7 – Probability of Compound Events Example 4 A card is drawn from a standard deck of 52 cards. Find the probability of each event. The card is not a 7. The card is not a red face card.

10.7 – Probability of Compound Events Example 5 There are 10 people at a dinner party. What is the probability that at least 2 people have the same birthday?

10.7 – Probability of Compound Events HOMEWORK 10.7 Practice A Worksheet