1 / 15

Section 11.7

Math in Our World. Section 11.7. The Addition Rules for Probability. Learning Objectives. Decide if two events are mutually exclusive. Use the addition rule for mutually exclusive events. Use the addition rule for events that are not mutually exclusive. Mutually Exclusive.

hafwen
Download Presentation

Section 11.7

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math in Our World Section 11.7 The Addition Rules for Probability

  2. Learning Objectives • Decide if two events are mutually exclusive. • Use the addition rule for mutually exclusive events. • Use the addition rule for events that are not mutually exclusive.

  3. Mutually Exclusive Two events are mutually exclusive if they cannot both occur at the same time. That is, the events have no outcomes in common. This indicates that either one or the other must occur, but not both.

  4. EXAMPLE 1 Deciding if Two Events Are Mutually Exclusive In drawing cards from a standard deck, determine whether the two events are mutually exclusive or not. • Drawing a 4, drawing a 6. • Drawing a 4, drawing a heart. SOLUTION (a) Every card has just one denomination, so a card can’t be both a 4 and a 6. The events are mutually exclusive. (b) You could draw the 4 of hearts, which is one outcome satisfying both events. The events are not mutually exclusive.

  5. Addition Rule 1 When two events A and B are mutually exclusive, the probability that A or B will occur is

  6. EXAMPLE 2 Using Addition Rule 1 A restaurant has three pieces of apple pie, five pieces of cherry pie, and four pieces of pumpkin pie in its dessert case. If a customer selects at random one kind of pie for dessert, find the probability that it will be either cherry or pumpkin.

  7. EXAMPLE 2 Using Addition Rule 1 SOLUTION The events are mutually exclusive. Since there is a total of 12 pieces of pie, five of which are cherry and four of which are pumpkin,

  8. EXAMPLE 3 Using Addition Rule 1 A card is drawn from a standard deck. Find the probability of getting an ace or a queen. SOLUTION The events are mutually exclusive. There are four aces and four queens; therefore,

  9. EXAMPLE 4 Using the Addition Rule with Three Events A card is drawn from a deck. Find the probability that it is either a club, a diamond, or a heart. SOLUTION The events are mutually exclusive. In the deck of 52 cards there are 13 clubs, 13 diamonds, and 13 hearts, and any card can be only one of those suits. So

  10. Addition Rule 2 When two events A and B are not mutually exclusive, the probability that A or B will occur is When two events are not mutually exclusive, any outcomes that are common to two events are counted twice. We account for this by subtracting the probability of both events occurring.

  11. EXAMPLE 5 Using Addition Rule 2 A single card is drawn from a standard deck of cards. Find the probability that it is a king or a club. SOLUTION In this case, there are 4 kings and 13 clubs. However, the king of clubs has been counted twice since the two events are not mutually exclusive.

  12. EXAMPLE 6 Using Addition Rule 2 Two dice are rolled. Find the probability of getting doubles or a sum of 6. SOLUTION First let’s review the possible outcomes.

  13. EXAMPLE 6 Using Addition Rule 2 SOLUTION There are six ways to get doubles. There are five ways to get a sum of 6. Notice that there is one way of getting doubles and a sum of 6.

  14. EXAMPLE 7 Using a Table andAddition Rule 2 In a hospital there are eight nurses and five physicians. Seven nurses and three physicians are females. If a staff person is selected, find the probability that the subject is a nurse or a male. SOLUTION The sample space can be written in table form.

  15. EXAMPLE 7 Using a Table andAddition Rule 2 SOLUTION Looking at the table, we can see that there are 8 nurses and 3 males, and there is one person who is both a male and a nurse. The probability is

More Related