Objective: Determine empirical probability based on specific sample data. (AA21)

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1 Do Now: What is an experiment? List some experiments. What types of things does one take a "chance" on? Mar 1 3:33 PM Date: Probability - Empirical - By Experiment Objective: Determine empirical probability based on specific sample data. (AA21) Feb 15 6:44 PM 1

2 Probability The chance that something will happen. Medicine, biology, genetics, manufacturing, gambling, and weather forecasting are just a few areas which use probability. Feb 9 8:55 PM Empirical Probability based on observations of a large number of trials the experiment is performed many times and the results are recorded. Feb 9 8:56 PM 2

3 TRIAL is a single attempt at doing something such as tossing a coin only once. An EXPERIMENT in probability is the repeating of the same trial many times. Feb 12 9:17 AM Fair Objects are objects that have not been weighted or made unbalanced. equal chance of happening Examples: coin, die Fair objects are also called unbiased objects. Feb 9 8:55 PM 3

4 Let's conduct an experiment to determine the probability of rolling a 5 with a six sided fair die. Feb 13 1:35 PM Student # of times a 5 is rolled # of rolls Cumulative # of times a 5 is rolled Cumulative # of spins Cumulative relative frequency Feb 12 2:31 PM 4

5 Biased Objects are objects that have been tampered with or weighted. chance of something happening is better one way than another. Example: two-headed coin weighted die Feb 9 8:57 PM Probability Theoretical In Theory Objective: Know the definition of conditional probability and use it to solve for probability in finite sample spaces. (AS18) Determine the number of elements in a sample space and the number of favorable events. (AS19) Mar 7 9:44 PM 5

6 Vocabulary Outcome is a result of some activity or experiment. (When rolling a die, 2 is an outcome) Sample Space is a set of all possible outcomes for the activity.(when rolling a die, the sample space is 1,2,3,4,5,6) Event is a subset of the sample space. (For example, odd numbers,even numbers, etc.) Favorable Event is obtaining the outcome you desire. Unfavorable Event is obtaining an outcome other than the one desired. Feb 13 2:13 PM Probability of an Event P(E) = n(e) n(s) = # of times event can occur total # of possible outcomes 0 P(E) 1 P(E) probability of an event n(e) # of successes (ways event may occur) n(s) total # of possible outcomes in sample space Feb 9 8:58 PM 6

7 Theoretical Probability Only for fair (unbiased) objects Outcomes - the result of some activity or experiment Sample Space - set of all possible outcomes for an activity or experiment Event - any subset of a sample space Sample Space Examples Coin heads tails Die - 1, 2, 3, 4, 5, 6 (Note: dice - more then one die) 7

8 Alphabet 26 letters 21 consonants 5 vowels (a, e, i, o, u) Standard Deck of Cards Feb 12 2:35 PM 8

9 Standard Deck of Cards 52 cards - 26 black/26 red 4 suits - 13, 13, 13, 13 4 of each A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K 12 face cards 4 kings, 4 queens, 4 jacks 1) Sid rolls a die. What is the probability of getting a number greater than 4? Event: rolling a # greater than 4 Outcomes: a 5 or 6 Sample space: 1, 2, 3, 4, 5, 6 9

10 2) Given a standard deck of 52 cards: A) What is the probability of drawing a Jack? B) What is the probability of drawing a heart? 3) A piggy bank contains a nickel, dime, and quarter. A person selects a coin at random. What is the probability that the coin is worth: a) exactly 10 b) exactly 3 c) more than 3 10

11 4) Subscripts are used in sample spaces to distinguish one object from another. P 1 R 1 O 1 B 1 A 1 B 2 I 1 L 1 I 2 T 1 Y 1 a) P(A) b) P(I) Let s try some! 1) P(tail) = 2) P(5 on a die) = 3) P(# 4 on a die) = 11

12 4) P(# < 4 on a die) = 5) P(even # on a die) = 6) P(prime # on a die) = 7) A letter is chosen at random from the word SUCCESS. a. P(U) = b. P(S) = c. P(vowel) = 12

13 Using a standard deck of cards: 8) P(jack) = 9) P(red card) = 10) P(face card) = 11) P(queen) = 12) P(diamond) = 13) P(heart) = 13

14 14) P(5) = 15) P(red card) = 16) A chess club consists of 90 members of whom 48 are boys and 42 are girls. If a member of the club is chosen at random to represent the club at a tournament, what is the probability that the person chosen is a boy? Feb 12 1:33 PM 14

15 Homework: pg. 581 #3 7 pg #3 9, 16, 20 Feb 12 1:37 PM 15