Geometry Unit 14 Probability Unit 14 Probability
Geometry Unit 14 ProbabilityUnit 14 ProbabilityTarget 1 – Calculate the probability of an eventTarget 2 – Calculate a sample space14.2a – Tree Diagrams, Factorials, and Permutations14.2b– CombinationsTarget 3 – Calculate the probability of independent and dependent events (compound) AND/THEN statementsTarget 4 – Calculate the probability of overlapping and disjoint events (mutually exclusive events14.4a – Addition Rule14.4b – Subtraction RuleTarget 5 – Calculate and apply conditional probabilityDateW 5-3R 5-4F 5-5M 5-8T 5-9W 5-10R 5-11F 5-12M 5-15T 5-16W 5-17R ReviewTestTestAssignmentDone!14.1 Worksheet14.2a Worksheet14.2b Worksheet14.3 WorksheetQuiz 14.1-14.314.4a Worksheet14.4b Worksheet14.5 WorksheetQuiz 14.4-14.5Unit 14 Test ReviewUnit 14 Test Part 1 (Targets 1-3)Unit 14 Test Part 2 (Targets 4-5, FRQ)Name:
Geometry Unit 14 Probability14.1– Experimental Probability &. Theoretical ProbabilityTarget 1: Calculate the probability of an eventVocabulary:Probability: The study of how likely it is that some event will occur.Experimental Probability: The number of times an event occurringdivided by the total number of observationsTheoretical Probability: determined using reasoning and analysisassuming the outcomes are equally likelySample Space: set of all possible outcomes of some action.Example 1: Find the experimental probability**P(A) is read: “The probability of event A occurring is”Surveyors counted the number of trees in a popular city park. Therewere 62 spruce trees, 44 firs, 12 oaks, and 2 maples. What is theexperimental probability that a randomly selected tree is an oak?Example 2: Find the theoretical probability using sample spaceIf a coin is flipped twice, it comes up heads twice. Use the samplespace to determine the theoretical probability of having twoheads in a set?Sample SpaceANNOTATE HERE
Geometry Unit 14 ProbabilityExample 3: Find the theoretical probability using sample spaceIf you roll a pair of dice, what is the probability that the total on thetwo dice will be 7?Sample SpaceYOU TRY NOW!1. A jar contains jellybeans, 5 of which are white, 14 blue, 18yellow, and 7 red. What is the theoretical probability ofgrabbing a blue jellybean?2. In a standard deck of cards there are 52 total cards. Four acesstandard deck. Johnny had 10 chances to select an ace fromthe deck. After each draw, Johnny put the card back into thedeck. The results are 9Draw105JQ8A36AK7What is the experimental probability of drawing an ace from adeck of cards?Answers:1.2.2ANNOTATE HERE
Geometry Unit 14 Probability14.2a – Tree Diagrams, Factorials, and PermutationsTarget 2: Calculate a sample spaceANNOTATE HEREFundamental Counting PrincipleNumber of outcomes Example 1: Find the number of outcomesThe Select Ice Creamer sells 8 flavors of ice cream and 3 types ofcones. How many single-scoop combinations can you buy?Vocabulary:Permutation: an ordered arrangement of a set of objects (ordermatters)
Geometry Unit 14 ProbabilityExample 2: Find the number of permutationsHow many permutations are there of the ten digits 0 through 9?ANNOTATE HEREExample 3: Find the number of permutations when a certain number of objectsare taken at a time100 people enter a contest where there is a first, second, and thirdprize. How many different ways are there for the prizes to beawarded assuming a person cannot be allowed to win more thanonce.“n objects chosen r at atime”YOU TRY NOW!1. A local restaurant offers a lunch buffet with 5 meats, 8vegetables, 3 breads, and 12 desserts. If a complete meal consistsof one of each, how many possible complete meals does therestaurant offer?2. How many different ways are there to choose jerseys for fiveathletes out of 30 possible numbers?3. Jan’s book club is choosing a one book to read in each of themonths December, January, and February. If there are 14 books tochoose from, how many permutations are there?Answers:1.2. 17,100, 720 ways3. 2184 permutations
Geometry Unit 14 Probability14.2b– CombinationsTarget 2: Calculate a sample spaceVocabulary:ANNOTATE HERECombination: a selection of elements of a set where the orderdoesn’t matter.Example 1: Find the number of combinationsHow many combinations of 2 cards can be formed from 4 cards ina deck?Example 2: Find the number of combinationsYou have 3 extra tickets to a concert by your favorite musician. Youhave 10 friends who would like to go. How many different groupscan you choose?r number objectschosen at a time.
Geometry Unit 14 ProbabilityYOU TRY NOW!1. How many two-letter groups can you form from the word MOUSEif you don’t care about the order?2. You need to choose three of your five friends for a trip. Howmany combinations can you choose from?3. How many different plates containing two pizza slices can beformed from a platter of pepperoni, sausage, mushroom, andcheese pizza if you can’t have two of the same slices on oneplate?Answers:1. 10 two letter groups2. 10 different friend groups of 33. 6 different platesANNOTATE HERE
Geometry Unit 14 Probability14.3 – Independent Events and the Multiplication RuleTarget 3: Calculate the probability of independent and dependent events (compound)AND/THEN statementsVocabulary:Independent Events: events in which the outcome of one has noANNOTATE HEREeffect on the probability of another occurring.Multiplication RuleWhen two independent events A and B,P(A and B) P(A) P(B)“AND”Example 1: Find the probability of independent events occurringWhat is the probability of a coin coming up heads twice?Example 2: Find the probability of independent events occurringA bag contains 11 marbles where 3 are red, 2 green, and 6 blue.You choose a marble from the bag, replace it, then draw again.What is the probability of drawing a red marble followed by agreen one?YOU TRY NOW!1. What is the probability of rolling a 2 or greater on a die, threetimes in a row?2. What is the probability that you draw two queens in a row from adeck of cards? You do not replace the card that you draw.Answers:a)b)
Geometry Unit 14 Probability14.4a – Addition RuleTarget 4: Calculate the probability of overlapping and disjoint events (mutually exclusiveeventsANNOTATE HEREVocabulary:Addition Rule: used to calculate the probability of event A or event Boccurring. P(A or B)“OR”Addition RuleThe probability of A or B equals the probability of A plus theprobability of B, minus the probability that A and B both occur.P(A or B) P(A)P(B) – P(A and B)Example 1: Find the probability that at least one event occursWhat is the probability that you roll a 6 on at least one of two dice?Example 2: Find the probability that at least one event occursOf 100 students surveyed, 95 like chocolates or raisins, 35 like bothchocolate and raisins, and 40 like raisins. How many student likechocolate?Example 3: Find the probability of mutually exclusive events using the additionruleWhat is the probability of choosing king or an ace from a standard52-card deck of playing cards?Mutually Exclusive:P(A and B) 0“Can’t have both eventsoccur at the same time.IMPOSSIBLE!”
Geometry Unit 14 ProbabilityYOU TRY NOW!1. The dogs at this shelter are all solid colors The probability that adog at this animal shelter is black is 0.4. The probability that it isyellow is 0.2.a) Is the event mutually exclusive?b) What is the probability that a dog at the shelter is black oryellow?2. A pair of dice is rolled.a)Is the event mutually exclusive?b)What is the probability that the sum of the numbersrolled is 7 or 11?3. A box contains three red playing cards numbered one to three.The box also contains five black playing cards numbered one tofive. You randomly pick a playing card.a)Is the event mutually exclusive?b)What is the probability that you chose a black or hasan odd number?Answers:1. a) Mutually Exclusiveb)2.a)b)Mutually Exclusive3.a)b)Not mutually exclusive0.875ANNOTATE HERE
Geometry Unit 14 Probability14.4b – Subtraction RuleTarget 4: Calculate the probability of overlapping and disjoint events (mutually exclusiveeventsANNOTATE HERESubtraction RuleThe probability of an event not occurring is 1 minus theprobability that it does occurThis also called finding thecomplement.P(not A) 1 – P(A)“NOT”Example 1: Find the probability of an event not occurringThe probability that Charlie catches a fish tomorrow is 0.3. What isthe probability that Charlie doesn’t catch a fish?Example 2: Find the probability of an event not occurringThe probability the toast lands butter side down is 0.85. What is theprobability it lands butter side up?YOU TRY NOW!1. If you roll two dice, there is a 1/6 probability that the sum will be7. What is the probability the two dice do not add to 7?Answer:
Geometry Unit 14 Probability14.5– Conditional ProbabilityTarget 5: Calculate and apply conditional probabilityVocabulary:ANNOTATE HEREConditional Probability: the probability of a second event occurring,given that the first event already occurred.Conditional ProbabilityThe probability of A occurring, given that B occurred equalsthe probability of both A and B occurring, divided by theprobability that B occurred.“given”“If”Example 1: Find the conditional probability given the probabilitiesThe probability that Sue will go to Mexico in the winter and toFrance in the summer is 0.40. The probability that she will go toMexico in the winter is 0.60. Find the probability that she will go toFrance this summer, given that she just returned from her wintervacation in Mexico.Equation todirectly applyP(A B) Example 2 Find the conditional probability using a VennDiagram or Frequency chartIn a monthly report, the local animal shelter states that it currentlyhas 24 dogs and 18 cats available for adoption. Eight of the dogsand 6 of the cats are male. Find the conditional probability if thepet selected is a male, given that it is a cat.
Geometry Unit 14 ProbabilityYOU TRY NOW!1. Andrea is a very good student. The probability that she studiesand passes her mathematics test is 17/20. If the probability thatAndrea studies is 15/16, find the probability that Andrea passes hermathematics test, given that she has studied.2. Out of 100 cars on a used car lot, 20 cars have manualtransmissions, 50 cars have air conditioning, and 8 cars have both.a) What is the percentage of cars that have air conditioninggiven they have manual transmissions?b) What is the percentage of cars that have manualtransmissions given they have air conditioning?Answers:1.2.a.b.ANNOTATE HERE
Target 4: Calculate the probability of overlapping and disjoint events (mutually exclusive events Subtraction Rule The probability of an event not occurring is 1 minus the probability that it does occur P(not A) 1 – P(A) Example 1: Find the probability of an event not occurring The pr
Joint Probability P(A\B) or P(A;B) { Probability of Aand B. Marginal (Unconditional) Probability P( A) { Probability of . Conditional Probability P (Aj B) A;B) P ) { Probability of A, given that Boccurred. Conditional Probability is Probability P(AjB) is a probability function for any xed B. Any
Pros and cons Option A: - 80% probability of cure - 2% probability of serious adverse event . Option B: - 90% probability of cure - 5% probability of serious adverse event . Option C: - 98% probability of cure - 1% probability of treatment-related death - 1% probability of minor adverse event . 5
Probability measures how likely something is to happen. An event that is certain to happen has a probability of 1. An event that is impossible has a probability of 0. An event that has an even or equal chance of occurring has a probability of 1 2 or 50%. Chance and probability – ordering events impossible unlikely
probability or theoretical probability. If you rolled two dice a great number of times, in the long run the proportion of times a sum of seven came up would be approximately one-sixth. The theoretical probability uses mathematical principles to calculate this probability without doing an experiment. The theoretical probability of an event
Engineering Formula Sheet Probability Conditional Probability Binomial Probability (order doesn’t matter) P k ( binomial probability of k successes in n trials p probability of a success –p probability of failure k number of successes n number of trials Independent Events P (A and B and C) P A P B P C
Chapter 4: Probability and Counting Rules 4.1 – Sample Spaces and Probability Classical Probability Complementary events Empirical probability Law of large numbers Subjective probability 4.2 – The Addition Rules of Probability 4.3 – The Multiplication Rules and Conditional P
Solution for exercise 1.4.9 in Pitman Question a) In scheme Aall 1000 students have the same probability (1 1000) of being chosen. In scheme Bthe probability of being chosen depends on the school. A student from the rst school will be chosen with probability 1 300, from the second with probability 1 1200, and from the third with probability 1 1500
In general, user-mode hooking is intended for API monitoring, like Mark Russinovich’s ProcessMonitor (alias FileMon/RegMon), resource leak detection, various malware which doesn’t need to care about security issues, extending applications and libraries you don’t have the source code for (also cracks may fall in this category), adding a compatibility layer for existing applications to run .
