1. Chapter 12 – Probability and Statistics 12.5 – Adding Probabilities

2. Today we will learn how to: Find the probability of mutually exclusive events Find the probability of inclusive events

3. 12.5 – Adding Probabilities Simple event – cannot be broken down into smaller events Rolling a die Compound event – an event consisting of two or more simple events Rolling an odd number or a number greater than 5

4. 12.5 – Adding Probabilities When you have two events, it’s important to understand how they are related before finding the probability of one or the other event occurring. Suppose you draw a card from a standard deck. What is the probability of drawing a 2 or an ace? Since a card cannot be both a 2 and an ace, these are called mutually exclusive Mutually exclusive – two events that cannot occur at the same time

5. 12.5 – Adding Probabilities The probability of drawing a 2 or an ace is found by adding their individual probabilities P (2 or ace) = P(2) + P(ace) = 4/52 + 4/52 = 8/52 or 2/13

6. 12.5 – Adding Probabilities Probability of Mutually Exclusive Events If two events, A and B, are mutually exclusive, then the probability that A or B occurs is the sum of their probabilities P(A or B) = P(A) + P(B)

7. 12.5 – Adding Probabilities Example 1 Sylvia has a stack of playing cards consisting of 10 hearts, 8 spades, and 7 clubs. If she selects a card at random from this stack, what is the probability that it is a heart or a club?

8. 12.4 – Multiplying Probabilities Example 2 The Film Club makes a list of 9 comedies and 5 adventure movies they want to see. They plan to select 4 titles at random to show this semester. What is the probability that at least two of the films they select are comedies?

9. 12.5 – Adding Probabilities Inclusive Events – When two events are not mutually exclusive The two events can occur at the same time Picking a king or a spade P(king) = 4/52 P(spade) = 13/52 P(king, spade) = 1/52 P(king or spade) / P(king) + P(spade) – P(king of spades) = 4/52 + 13/52 – 1/52 = 4/13

10. 12.5 – Adding Probabilities Probability of Inclusive Events If two events, A and B, are inclusive, then the probability that A or B occurs in the sum of their probabilities decreased by the probability of both occurring. P(A or B) = P(A) + P(B) – P(A and B)

11. 12.5 – Adding Probabilities Example 3 There are 2400 subscribers to an Internet service provider. Of these, 1200 own Brand A computers, 500 own Brand B, and 100 own both A and B. What is the probability that a subscriber selected at random owns either Brand A or Brand B?

12. 12.5 – Adding Probabilities HOMEWORK Page 713 #11 – 29 odd, #30 – 38