4.2 SOME PROBABILITY RULES –COMPOUND EVENTS PART 2: ADDITION RULES Chapter 4: Elementary Probability Theory
Page 147 Multiplication VS Addition Multiplication Addition Rules are Rules are used to used to find the find the probability probability of one of two events event or another Notice the happening occurring. condition A or B together. is satisfied by any of the following: 1. Any outcome in A occurs 2. Any outcome in B occurs The Event A and B The Event A or B 3. Any outcome Figure 4-4(a) Figure 4-4 (b) in both A and B occurs
PageExample – Combining Events 148 Indicate how each of the following pairs of events are combined. Use either the and combination or the or combination. a) Satisfying the humanities requirement by taking a course in the history of Japan or by taking a course in classical literature. b) Buying new tires and aligning the tires. c) Getting an A not only in psychology but also in biology. d) Having at least one of these pets: cat, dog, bird, rabbit.
Be Careful! Page Do Not confuse 149Addition Rules “independence” with “mutually exclusive” Two events are mutually exclusive or disjoint if they cannot occur together. In particular, events A and B are mutually exclusive if P(A and B) = 0. Addition Rule for Mutually Exclusive EventsThe addition rule for mutually exclusive P(Aevents can be expandedP(B) adding! or B) exclusive events… keep than two mutually = P(A) + for more (page 151) General Addition Rule for ANY Events
Page 150How to Use the Addition Rules1. Determine whether A and B are mutually exclusive events. If P(A and B) = 0, then the events are mutually exclusive2. If A and B are mutually exclusive events P(A or B) = P(A) + P(B)3. If A and B are not mutually exclusive events P(A or B) = P(A) + P(B) – P(A and B)
PageExample 6 – Probability of Events 148Combined with OR Consider an introductory statistics class with 31 students. The students range from freshmen through seniors. Some students are male and some are female. Figure 4-5 shows the sample space. a) Suppose we select one student at random from the class. Find the probability that the student is either a freshman or a sophomore. b) Select one student at random from the class. What is the probability that the student is either a male Sample Space for Statistics Class or a sophomore? Figure 4-5
PageExample 7 – Mutually Exclusive 151Events Laura is playing Monopoly. On her next move she needs to throw a sum bigger than 8 on the two dice in order to land on her own property and pass Go. What is the probability that Laura will roll a sum bigger than 8?
Solution – Mutually Exclusive Events When two dice are thrown, the largest sum that can come up is 12. Consequently, the only sums larger than 8 are 9, 10, 11, and 12. These outcomes are mutually exclusive, since only one of these sums can possibly occur on one throw of the dice.P(9 or 10 or 11 or 12) = P(9) + P(10) + P(11) + P(12)
Page Summary of Basic Probability 154 Rules Use this chart!! Also See Table 4-3 “English Phrases and Corresponding Symbolic Translations”