ANNOUNCEME NTS -Pick up your assigned calculator -Take out HW to stamp WARM UP 1.Copy the following into your Vocab Section (Purple tab!) Independent Events – involves two or more events in which the outcome of one event DOES NOT affect the outcome of any other events Dependent Events – involves two or more events in which the outcome of one event DOES affect the outcome of the other events Mutually Exclusive – two events cannot happen at the same time 2.Update your TOC.

#3 Compound Probability

Practice: Determine if the events are Independent or Dependent 1.Roll a die, then spin a spinner. 2.Pick one flash card, then another from the same stack of 30 flash cards without replacing it. 3.You select a coin at random from your pocket. You replace the coin and select again. Independent Dependent

Independent Events Independent Events – involves two or more events in which the outcome of one event DOES NOT affect the outcome of any other events EXAMPLE: Your grade in Math class and your grade in English class The final score of a hockey game played in Los Angeles, and the final score of a basketball game played in New York

Example 1: P(jack, factor of 12) x= Independent Events

Example 2: You roll a red number cube and a blue number cube. What is the probability that you roll a 5 on the red cube and a 1 or 2 on the blue cube? The probability of rolling a 5 on the red number cube is __________. The probability of rolling a 1 or 2 on the blue number cube is ______________. Find the probability of rolling a 5 on the red cube AND a 1 or 2 on the blue cube.

Dependent Events Dependent Events – involves two or more events in which the outcome of one event DOES affect the outcome of the other events Examples: Drawing from the same deck of cards Selecting items from a container without replacement

Example 3: P(Q, S) All the letters of the alphabet are in the bag 1 time Do not replace the letter x= Dependent Events

Example 4: One freshman, 2 sophomores, 4 juniors, and 5 seniors receive top scores in a school essay contest. To choose which 2 students will read their essays at the town fair, 2 names are chosen at random from a hat. What is the probability that a senior and then a junior are chosen? Are the events of choosing a senior and then a junior independent or dependent? The probability that a senior is chosen first is __________. The probability that a junior is chosen after a senior is chosen is ______________. What is the probability that a senior and then a junior is chosen?

Are these independent or dependent events? Independent = hands on handDependent = hands to the sky 1.Tossing two dice and getting a 6 on both of them. 2.You pick the letter Q from a bag containing all the letters of the alphabet. You do not put the Q back in the bag before you pick another tile. 3.Pick one flash card, put it back in the stack, then pick another from the same stack of 30 flash cards. 4.You have a basket of socks. You need to find the probability of pulling out a black sock and its matching black sock without putting the first sock back. independent dependent independent dependent

BRAIN BREAK #1

FORMULAS

Example 5: At a picnic, there are 10 diet drinks and 5 regular drinks. There are also 8 bags of fat-free chips and 12 bags of regular chips. If you grab a drink and a bag of chips without looking, what is the probability that you get a diet drink and fat-free chips? ∙

Practice Problem: Using the information in #5, what is the probability that you get a regular drink and regular chips? At a picnic, there are 10 diet drinks and 5 regular drinks. There are also 8 bags of fat-free chips and 12 bags of regular chips. ∙

FORMULAS

You roll a standard die. are the events mutually exclusive? 6. Rolling a 2 and a 37. Rolling an even number and a multiple of 3 8. Rolling an even number9. Rolling an even number and and rolling prime number rolling a number less than 2 Mutually Exclusive Not Mutually Exclusive Can roll a 6 Not Mutually Exclusive  Can roll a 2

a. Round or Green? b. Orange or Triangle?c. Yellow or Square? Example 10: Suppose you reach into a dish and select a token at random. What is the probability that the token is: + not mutually exclusive because they do happen at the same time mutually exclusive because they do not overlap

BRAIN BREAK #2

Homework #3 in HW Packet (top of pg. 2 – all) HW Packets due Tuesday, 5/26!

Quantitative Comparison: Which probability is greater? QUANTITY A P(rolling a # greater than 5 on a fair die or rolling a # that is not even) QUANTITY B P(rolling a 2 on a fair die and rolling an odd # on a fair die) A: Quantity A is greater B: Quantity B is greater C: They are the same D: Not enough information “or” means ADD! “and” means MULTIPLY!