1.6 Probability9.7 Probability of Multiple Events 12.2 Conditional Probability

Measures how likely it is that an event will occur. Probability Measures how likely it is that an event will occur. Expressed as A Percentage (0-100%) or a number between 0 and 1

Lesson Notes 9.7 and 12.2 Probability Examples Experimental Probability Lesson Notes 9.7 and 12.2 Probability Examples Experimental Probability: Based on observation Ex1) A quarterback throws 40 passes during a game and completes 30 of them. Find the experimental probability of him completing a pass.

Lesson Notes 9.7 and 12.2 Probability Examples Theoretical Probability Lesson Notes 9.7 and 12.2 Probability Examples (Theoretical) Probability: Based on what would happen in theory. Ex2) Find the probability of rolling a prime number when you roll a regular six-sided die.

Example from Venn diagram Ex 3) What is the probability of drawing a heart that is not a face card from a deck of 52 cards. Everything else Hearts Face Cards

Lesson Notes 9.7 and 12.2 Probability Examples 9.7 Probability of Multiple Events Lesson Notes 9.7 and 12.2 Probability Examples Compound Events Independent Events (One event does not affect another event) Dependent Events (One event affects another event) 6

Lesson Notes 9.7 and 12.2 Probability Examples Probability that both Independent Events will occur: 1 2 3 Ex 4) What is the probability of spinning a 3 on the spinner and rolling a 3 on the die? 7

Lesson Notes 9.7 and 12.2 Probability Examples Compound Events Ex 5) A card is drawn from a standard 52-card deck. Then a die is rolled. Find the probability of each compound event. P(draw heart and roll 6) P(draw 7 and roll even P ( draw face card and roll < 6) 8

Lesson Notes 9.7 and 12.2 Probability Examples Compound Events Lesson Notes 9.7 and 12.2 Probability Examples Ex 6) There are five discs in a CD player. The player has a “random” button that selects songs at random and does not repeat until all songs are played. What is the probability that the first song is selected from disc 3 and the second song is selected from disc 5? Disc 1 8 songs Disc 2 10 songs Disc 5 10 songs Disc 4 9 songs Disc 3 13 songs 9

Lesson Notes 9.7 and 12.2 Probability Examples Why are these independent events? Ex 7) A drawer contains 4 green socks and 5 blue socks. One sock is drawn at random. Then another sock is drawn at random. a. Suppose the first sock is returned to the drawer before the second is drawn at random. Find the probability that both are blue. b. Suppose the first sock is not returned to the drawer before the second is drawn. Find the probability that both are blue. 10

Lesson Notes 9.7 and 12.2 Probability Examples Probability with “OR” What is the probability event A or event B could occur? Mutually Exclusive Events: two events that CANNOT happen at the same time If A and B are mutually exclusive events, then If A and B are not mutually exclusive events, then Subtract the overlap 11

Lesson Notes 9.7 and 12.2 Probability Examples OR Lesson Notes 9.7 and 12.2 Probability Examples Example 8) P(face card) = P(non-face card) = P(face card or ace) = P(two or card < 6) = P(not a jack) = P(red card or seven) = P(ace or king) = 12

HW Assignment Section 6.7 “Basic” Probability p. 42 #6-14 (even), 25-33 Section 9.7 “multiple event” Probability p. 534 #1,2, 5, 9, 13, 16, 19-25 (odd),37,39,45 p. 542 #36 Section 12.2 “Conditional” Probability p. 136 #1-13 all

Lesson Notes 9.7 and 12.2 Probability Examples Yes, Did a chore last night No, Did NOT do a chore Male 2 7 Female 6 3 14

Lesson Notes 9.7 and 12.2 Probability Examples Section 12.2: Conditional Probability Lesson Notes 9.7 and 12.2 Probability Examples Conditional Probability Formula: “Probability of event B, given that event A has occurred” “given” Yes, Did a chore last night No, Did NOT do a chore Male 2 7 Female 6 3 Ex 10) 15

Lesson Notes 9.7 and 12.2 Probability Examples Conditional Probability Ex 11) A cafeteria offers vanilla and chocolate ice cream, with or without fudge sauce. The manager kept records on the last 200 customers who ordered ice cream. Fudge Sauce No Fudge Sauce Total Vanilla Ice Cream 64 68 132 Chocolate Ice Cream 41 27 105 95 200 a. P(includes fudge sauce) b. P(includes fudge sauce | chocolate ice cream) c. P(chocolate ice cream | includes fudge sauce) 16

Lesson Notes 9.7 and 12.2 Probability Examples Conditional Probability Fudge Sauce No Fudge Sauce Total Vanilla Ice Cream 64 68 132 Chocolate Ice Cream 41 27 105 95 200 d. P(vanilla ice cream with no fudge sauce) e. P(vanilla ice cream | does not include fudge sauce) f. Find the probability that the order has no fudge sauce, given that it has vanilla ice cream. 17

Tree Diagrams – Ex 12)