Exercise 124 Probability Of Disjoint And Overlapping Events
Vocabulary and Core Concept Check
Question 1.WRITINGAre the events A and \ disjoint? Explain. Then give an example of a real-life event and its complement.Answer:Yes A and \ are disjoint events because they are the complement of one another and so can not occur together and hence the name disjoint.Example:So, A = \ = are disjoint events.
Question 2.Which is different? Find both answers.How many outcomes are in the intersection of A and B?Answer: There are 2 outcomes in the intersection of A and B.
How many outcomes are shared by both A and B?Answer: 2 outcomes are shared by both A and B.
How many outcomes are in the union of A and B?Answer: There are 4 + 2 + 3 = 9 outcomes in the union of A and B.
How many outcomes in B are also in A?Answer: There are 2 outcomes in B that are also in A.
Monitoring progress and Modeling with Mathematics
In Exercises 3 6, events A and B are disjoint. Find P
Question 3.
P = P + PP = 0.55 + 0.2 = 0.75
Question 5.P = \, P = \Answer:
p = \, P = \Answer:p = \, P = \P = P + PP = \ + \P = \
Question 7.PROBLEM SOLVINGYour dart is equally likely to hit any point inside the board Shown. You throw a dart and pop a balloon. What is the probability that the balloon is red or blue?Answer:
ERROR ANALYSISIn Exercises 11 and 12, describe and correct the error in finding the probability of randomly drawing the given card from a standard deck of 52 playing cards.
Question 11.
In Exercises 13 and 14, you roll a six-sided die. Find P.
Writing a Conjecture
Big Ideas Math Book Geometry Answer Key Chapter 12 Probability
Most of the students think that probability is the toughest chapter in maths. But if you understand the logic this will be the easiest of all the chapters. Click on the below attached links and start practicing the problems. Learn the concepts in depth and test your knowledge by solving the questions given at the end of the chapter.
Taking the inverse of both sidesx%/100% = 34.4/86Therefore, 34.4 is 40% of 86.
Display the data in a histogram.
Question 4.
Question 5.ABSTRACT REASONINGYou want to purchase either a sofa or an arm chair at a furniture store. Each item has the same retail price. The sofa is 20% off. The arm chair is 10% off. and you have a coupon to get an additional 10% off the discounted price of the chair. Are the items equally priced after the discounts arc applied? Explain.Answer: Yes
Explanation:You want to purchase either a sofa or an armchair at a furniture store.Each item has the same retail price. The sofa is 20% off. The armchair is 10% off. and you have a coupon to get an additional 10% off the discounted price of the chair.The price of armchair and sofa are the same.If you add 10% to chair the discount for the chair and sofa will be the same.10% + 10% = 20%
Lesson 125 Permutations And Combinations
Monitoring Progress
In how many ways can you arrange the letters in the word HOUSE?Answer:
In how many ways can you arrange 3 of the letters in the word MARCH?Answer:
Question 3.WHAT IFIn Example 2, suppose there are 8 horses in the race. In how many different ways can the horses finish first, second, and third? Answer:
Question 4.WHAT IF?In Example 3, suppose there are 14 floats in the parade. Find the probability that the soccer team is first and the chorus is second.Answer:
Question 5.Count the possible combinations of 3 letters chosen from the list A, B, C, D, E.Answer:
Question 6.WHAT IF?In Example 5, suppose you can choose 3 side dishes out of the list of 8 side dishes. How many combinations are possible?Answer:
Question 7.WHAT IF?In Example 6, suppose there are 20 photos in the collage. Find the probability that your photo and your friends photo are the 2 placed at the top of the page.Answer:
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Why To Read Geometry Bigideas Math Answer Key
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Sample Spaces And Probability
Exploration 1
Finding the Sample Space of an Experiment
Work with a partner: In an experiment, three coins are flipped. List the possible outcomes in the sample space of the experiment.Answer:The number of different outcomes when three coins are tossed is 2 × 2 × 2 = 8.All 8 possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH and TTT.
Exploration 2
Finding the Sample Space of an Experiment
Work with a partner: List the possible outcomes in the sample space of the experiment.
a. One six-sided die is rolled.Answer: 6 possible outcomes
b. Two six-sided die is rolled.Answer:Rolling two six-sided dice: Each die has 6 equally likely outcomes, so the sample space is 6 . 6 or 36 equally likely outcomes.
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Geometry Terms 2 And 4
Chapter 5 ;Midsegments, Medians, Angles Bisectors, Perpendicular Bisectors, Altitudes
Chapter 5 Review Click;HERE
Chapter 5 Review Answer Key Click;HERE
Chapter 5 Review #2 Click;HERE
Chapter 5 Review #2 Answer Key Click;HERE
Chapter 7 ;Pythagorean Theorem, Special Right Triangles, and Trigonometry;
Chapter 7 Review Click;HERE
Chapter 7 Review Answer Key Click;HERE
Cumulative Review Chapters 5 and 7
Ch 5 and 7 Cumulative Review Packet Click;HERE
Ch 5 and 7 Cumulative Review Packet Answer Key Click;HERE
Chapter 8 Quadrilaterals
Chapter 8 Review Click;HERE
Chapter 8 Review Answer Key Click;HERE
Chapter 10 Circles, Tangents, Secants, Arcs
10.1 PowerPoint Presentation Notes ;Click ;HERE
10.1 Worksheet A Click ;HERE
10.2 PowerPoint Presentation Notes Click ;HERE
10.2 Worksheet B Click ;HERE
10.3 PowerPoint Presentation Notes Click ;HERE
10.3 Worksheet A Click ;HERE
10.4 PowerPoint Presentation Notes Click;HERE
10. 4 Inscribed Angles GeoGebra Demonstration ;Click;HERE
10.4 Worksheet Click ;HERE
10.5 PowerPoint Presentation Notes Click;HERE
10.5 Chord Properties Investigation Worksheet Click;HERE
10.5 Chord Properties Worksheet Day 2 Click ;HERE
10.6 PowerPoint Presentation Notes Click;HERE
10.6 Practice Examples Click;HERE
10.7 PowerPoint Presentation Notes Click;HERE
10.7 Worksheet A Click;HERE
Chapter 10 Review Click;HERE
Chapter 10 Review Answer Key Click;HERE
Cumulative Review Chapters 8 and 10
11.1 Worksheet A Click;HERE
Exercise 122 Independent And Dependent Events
Vocabulary and Core Concept Check
Question 1.Explain the difference between dependent events and independent events, and give an example of each.Answer:When two events are dependent, the occurrence of one event affects the other. When two events are independent, the occurence of one event does not affect the other.
Question 2.COMPLETE THE SENTENCEThe probability that event B will occur given that event A has occurred is called the _____________ of B given A and is written as _____________ .Answer:The probability that event B will occur given that event A has occurred is called the conditional probability of B given A and is written as P.
Monitoring Progress and Modeling with Mathematics
In Exercises 3 6, tell whether the events are independent or dependent. Explain your reasoning.
Question 3.A box of granola bars contains an assortment of flavors. You randomly choose a granola bar and eat it. Then you randomly choose another bar.Event A: You choose a coconut almond bar first.Event B: You choose a cranberry almond bar second.Answer:The two events, which considered in this experiment are an example of dependent events.
Question 4.You roll a six-sided die and flip a coin.Event A: You get a 4 when rolling the die.Event B: You get tails when flipping the coinAnswer: Independent, the events do not influence each other.
In Exercises 7 10. determine whether the events are independent.
0.3x \x + 1.6 = 1.555Answer:
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Probability Of Disjoint And Overlapping Events
Exploration 1
Work with a partner: A six-sided die is rolled. Draw a Venn diagram that relates the two events. Then decide whether the cents are disjoint or overlapping.MODELING WITH MATHEMATICSTo be proficient in math, you need to map the relationships between important quantities in a practical situation using such tools as diagrams.a. Event A: The result is an even number.Event B: The result is a prime number.Answer:
b. Event A: The result is 2 or 4.Event B: The result is an odd numberAnswer:
Exploration 2
Finding the Probability that Two Events Occur
Work with a partner: A six-sided die is roiled. For each pair of events. find P, P. P and . and P.a. Event A: The result is an even number.Event B: The result is a Prime number.Answer:P = \ = \P = \ = \P = P + P PP = \P = \
b. Event A: The result is 2 or 4.Event B: The result is an odd number.Answer:P = \ = \P = \ = \P = P + P PP = 0P = \
Exploration 3
Discovering Probability Formulas
Work with a partner:a. In general, if event A and event B arc disjoint, then what is the probability that event A or event B will occur? Use a Venn diagram to justify your conclusion.Answer:If event A and B are disjoint, there are no common outcomes.So we add the probabilities that each event occurs:P = P + P
Communicate Your Answer
Question 5.Give examples of disjoint events and overlapping events that do not involve dice.Answer:
a. Event A: The result is an even number.Event B: The result is a prime number.Answer:
Exercise 125 Permutations And Combinations
Vocabulary and Core Concept Check
Question 1.An arrangement of objects in which order is important is called a _________ .Answer:An arrangement of objects in which order is important is called a Permutation.
Question 2.WHICH ONE DOESNT BELONG?Which expression does not belong with the other three? Explain your reasoning.\ 7C57C2 \Answer:7C2 \ = \= 7C2The expression \ does not belong with other three.
Monitoring Progress and Modeling with Mathematics
In Exercises 3 8, find the number of ways you can arrange all of the letters and 2 of the letters in the given word.
Question 3.
TRYAnswer:a. In this case, we have to find the number of permutations all of the letters in a given word that will consist of 3 letters.Number of permutations = × × = 3 . 2 . 1 = 6Therefore we have 6 ways for arrange all of the letters in given word, that is TRY, TYR, YTR, YRT, RTY and RYT.Now, we have to find the number of permutation 2 of the letters in a given word that will consists of 3 lettersNumber of permutations = × = 3 . 2 = 6We have 6 ways for arrange 2 of the letters in given word, tthat is TR, TY, YT, YR, RT and RY.
Question 5.
Question 7.
In Exercises 9 16, evaluate the expression.
Question 9.
= 6 . 5 . 4 . 3 . 2 . 16P6;= 720
In Exercises 21 24, count the possible combinations of r letters chosen from the given list.
Question 21.A, B, C, D; r = 3Answer:
L, M, N, O; r = 2Answer:
20C5 = \= \ . \= 20 . 19 . 18 . 17 . 16 . 15 . 8 . 7 . 6 . 5 . 4 . 3 . 2 . 1/ = 19 . 3 . 17 . 16
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Big Ideas Math Geometry Answers Chapter 12 Probability
Get the pdf link of Big Ideas Math Geometry Answers Chapter 12 Probability from this page. The concepts to learn in Probability are Sample Spaces and Probability, Independent and Dependent Events, Two-Way Tables and Probability, Probability of Disjoint and Overlapping Events and Permutations and Combinations, Binomial Distributions. Get step by step explanations for all the questions from Big Ideas Math Answers Geometry Chapter 12 Probability.
Exercise 121 Sample Spaces And Probability
Vocabulary and Core Concept Check
Question 1.A number that describes the likelihood of an event is the ___________ of the event.Answer:A number that describes the likelihood of an event is the Probability of the event.
Question 2.WRITINGDescribe the difference between theoretical probability and experimental probability.Answer: Experimental probability is the result of an experiment. Theoretical probability is what is expected to happen.
Monitoring Progress and Modeling with Mathematics
In Exercises 3 6. find the number of possible outcomes in the sample space. Then list the possible outcomes.
Question 3.You roll a die and flip three coins.Answer:
Question 4.You flip a coin and draw a marble at random from a hag containing two purple marbles and one while marble.Answer:Given data,You flip a coin and draw a marble at random from a hag containing two purple marbles and one while marble.the probability of getting a purple marble = 2/3the probability of getting a white marble = 1/3
Question 5.A bag contains four red cards numbered 1 through 4, four white cards numbered 1 through 4, and four black cards numbered 1 through 4. You choose a card at random.Answer:
Question 7.PROBLEM SOLVINGA game show airs on television five days per week. Each day, a prize is randomly placed behind one of two doors. The contestant wins the prize by selecting the correct door. What is the probability that exactly two of the five contestants win a prize during a week?Answer:
Question 29.\Answer:
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Independent And Dependent Events
Exploration 1
Identifying Independent and Dependent Events
Work with a partner: Determine whether the events are independent or dependent. Explain your reasoning.REASONING ABSTRACTLYTo be proficient in math, you need to make sense of quantities and their relationships in problem situations.a. Two six-sided dice are rolled.Answer:P = Number of outcomes that satisfy the requirements/Total number of possible outcomesProbability for rolling two dice with the six sided dots such as 1, 2, 3, 4, 5 and 6 dots in each die.When two dice are thrown simultaneously, thus the number of event can be 62 = 36 because each die has 1 to 6 number on its faces.This is independent event
b. Six pieces of paper, numbered 1 through 6, are in a bag, Two pieces of paper are selected one at a time without replacement.Answer:P = Number of outcomes that satisfy the requirements/Total number of possible outcomesWhen we pick up any paper the probability result is equal of 1/6This is dependent event
Exploration 2
Work with a partner:
a. In Exploration 1, experimentally estimate the probability that the sum of the two numbers rolled is 7. Describe your experiment.Answer:
. In Exploration 1 , experimentally estimate the probability that the sum of the two numbers selected is 7. Describe your experiment.Answer:
Finding Theoretical Probabilities
C. Compare the probabilities you obtained in parts and .Answer:
Lesson 122 Independent And Dependent Events
Monitoring progress
Question 1.In Example 1, determine whether guessing Question 1 incorrectly and guessing Question 2 correctly are independent events.Answer:
Question 2.In Example 2, determine whether randomly selecting a girl first and randomly selecting a boy second are independent events.Answer:
Question 3.In Example 3, what is the probability that you spin an even number and then an odd number?Answer:
In Example 4, what is the probability that both hills are $1 hills?Answer:
Question 5.In Example 5, what is the probability that none of the cards drawn are hearts when you replace each card, and you do not replace each card? Compare the probabilities.Answer: you replace each card,P = P P P= 13/52 . 13/52 . 13/52 = 1/4 . 1/4 . 1/4 = 1/64 = 0.016
Question 6.In Example 6, find the probability that a non-defective part passes and the probability that a defective part fails.Answer: the probability that a non-defective part passesP = 3/39 = 1/13 = 0.077 the probability that a defective part fails.P = 11/461 = 0.024
Question 7.At a coffee shop. 80% of customers order coffee. Only 15% of customers order coffee and a bagel. What is the probability that a customer who orders coffee also orders a bagel?Answer:B: Customer order a bagelP = P/P80% of customers order coffee and Only 15% of customers order coffee and a bagel.P = 80/100 = 0.8P = 15/100 = 0.15P = P/P = 0.15/0.8 = 0.1875 = 18.75%
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Lesson 121 Sample Spaces And Probability
Monitoring Progress
Find the number of possible outcomes in the sample space. Then list the possible outcomes.
Question 1.Answer: 4
Explanation:When we flip two coins simultaneoulsy then the possible outcomes will be , , , where H represents headsThus the possible outcomes are 2² = 4
Question 2.You flip two Coins and roll a six-sided die.Answer: 6 × 2² = 24
Explanation:We roll a die and flip two coins. We have to find the number of possible outcomes in this space. Also we have to list the possible outcomes.1 = ;2 = ;3 = ;4 = ;5 = ;6 = ;On the other hand, using H for Heads and T for Tails we can list the outcomes., , , , , , , , , , , , , , , , , , , , Therefore, we can conclude that the number of all possible outcomes is6 × 2² = 24
Question 3.You flip a coin and roll a six-sided die. What is the probability that the coin shows tails and the die shows 4?Answer:The sample space has 12 possible outcomes.Heads, 1
More likely to get 2 points.
Question 10.In Example 5, for which color is the experimental probability of stopping on the color greater than the theoretical probability?Answer:9/20 = 0.45
Question 11.In Example 6, what is the probability that a pet-owning adult chosen at random owns a fish?Answer:
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