Chapter 9 Section 7 Chapter 12 Section 2 Algebra 2 Notes February 12, 2009

Warm-Ups What is the probability that you will roll exactly five sixes in ten tosses of a standard die? 6% of the circuit boards assembled at a certain production plant are defective. If five circuit boards are chosen at random, what is the probability that exactly two are defective?

SECTION 9.7 Probability of Multiple Events

Multiple Events Dependent Event: When the outcome of one event affects the outcome of a second event Examples: ◦ Pick a flower from a garden. Then pick another flower from the same garden. ◦ Select a marble from a bag of multicolored marbles. Put that marble aside ad select a second marble from the same bag.

Multiple Events Independent Events: When the outcome of one event does not affect the outcome of a second event. Examples: ◦ Rolling a standard die and then flipping a coin ◦ Spin a spinner, then select a marble from a bag of multicolored marbles. ◦ Select a marble from a bag of marbles. Replace the marble and then select again

Independent Events Suppose that A and B are independent events. Then:

Independent Events Example 1: A box contains 20 red marbles and 30 blue marbles. A second box contains 10 white marbles and 47 black marbles. If you choose one marble from each box without looking, what is the probability that you get one blue marble and one black marble?

Independent Events Example 2: Suppose your favorite radio station is running a promotional campaign. Every hour, four callers chosen at random get to compete to win $100!! You call the radio station once after 7:00am and again after 3:00pm. What is the probability that you will be one of the four callers both times you call? HOURCALLS RECEIVED THAT HOUR 7:00 A.M.125 3:00 P.M.200

Mutually Exclusive Events Mutually Exclusive Events: Two events that cannot happen at the same time ◦ If A and B are mutually exclusive events, then P(A and B) = 0 Determine if each event is mutually exclusive: ◦ Rolling a 2 or a 3 on a standard die ◦ Rolling an even number or a multiple of 3 on a standard die

Probability of (A or B) If A and B are mutually exclusive events: If A and B are not mutually exclusive events

Probability of (A or B) Example 1: About 53% of U.S. college students are under 25 years old. About 21% of U.S. college students are over 34 years old. What is the probability that a college student chosen at random is under 25 or over 34? Example 2: Suppose you reach into a bowl of 3 red apples, 3 green apples, 1 lime, 1 lemon, and 2 oranges. What is the probability that the fruit is an apple or green?

Quick Note When the problem asks you to find the probability of event A and event B, you will multiply the two probabilities When the problem asks you to find the probability of event A or event B, you will add the two probabilities

SECTION 12.2 Conditional Probability

Finding Conditional Probability Conditional Probability: contains a condition that may limit the sample space for an event. ◦ Write as which stands for “the probability of event B, given event A.”

Finding Conditional Probability The following table shows the results of a class survey. Find the conditional probability: Did you do a chore last night? YESNO MALE78 FEMALE76

Conditional Probability Formula Researchers asked shampoo users whether they apply shampoo directly to the head or indirectly using a hand. Find the probability that a respondent applies shampoo directly to the head, given the respondent is female. Applying Shampoo Directly to Head Into Hand First MALE218 FEMALE624

Conditional Probability Formula Eighty percent of airline flights depart on schedule. Seventy-two percent of its flights depart and arrive on schedule. Find the probability that a flight that departs on time also arrives on time.

Making a Tree Diagram A student in Buffalo, New York, made the observations below: ◦ Of all snowfalls, 5% are heavy (at least 6 in.) ◦ After a heavy snowfall, schools are closed 6% of the time ◦ After a light snowfall (less than 6 in.) schools are closed 3% of the time. Find the probability that the snowfall is light and the schools are open.

Homework #23 Pg 534 #1, 2, 5, 6, 9-11, 14, 15, 18, 19, 24, 25, Pg 656 #1-9, 11, 12, 20, 21