9.7 Probability of Multiple Events 12.2 Conditional Probability

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Presentation transcript:

9.7 Probability of Multiple Events 12.2 Conditional Probability Small opportunities are often the beginning of great enterprises.

Compound Events Compound Events Independent Events (One event does not affect another event) Dependent Events (One event affects another event) 2

Compound Events Probability of Independent Events: 1 2 3 Ex1) What is the probability of spinning a 3 on the spinner and rolling a 3 on the die? 3

Compound Events Ex2) A card is drawn from a standard 52-card deck. Then a die is rolled. Find the probability of each compound event. a) P (draw heart and roll 6) b) P (draw 7 and roll even) c) P (draw face card and roll < 6) 4

Compound Events Ex3) 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. 5

Compound Events Mutually Exclusive Events: two events that CANNOT happen at the same time. Probability with “OR”: If A and B are mutually exclusive events, then If A and B are not mutually exclusive events, then 6

Ex4) Practice Problems 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) = 7

Conditional Probability Conditional Probability Formula: For any two events A and B from a sample space with , “given” The table shows the results of a class survey. Ex5) Find P(own a pet | female) 8

Conditional Probability Ex6) 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) 9

Conditional Probability Fudge Sauce No Fudge Sauce Total Vanilla Ice Cream 64 68 132 Chocolate Ice Cream 41 27 105 95 200 c. P(chocolate ice cream | includes fudge sauce) d. P(vanilla ice cream with no fudge sauce) e. P(vanilla ice cream | does not include fudge sauce) 10

Conditional Probability Fudge Sauce No Fudge Sauce Total Vanilla Ice Cream 64 68 132 Chocolate Ice Cream 41 27 105 95 200 e. Find the probability that the order has no fudge sauce, given that it has vanilla ice cream. f. P(vanilla ice cream) 11

Tree Diagrams Ex 7) A student made the following observations of the weather in his hometown. On 28% of the days, the sky was mostly clear. During the mostly clear days, it rained 4% of the time. During the cloudy days it rained 31% of the time. a. Use a tree diagram to find the probability that a day will start out clear, and then it will rain. b. Find the probability that it will not rain on any given day.

9.7 Probability of Multiple Events 12.2 Conditional Probability HW: pg. 534 #1-7 odd, 11-25 odd, 31-39 odd pg. 656 #1-13 all Small opportunities are often the beginning of great enterprises.