Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
6th Edition
ISBN: 9780321914620
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Chapter 7.B, Problem 48E
Assorted Probabilities. Use the method of your choice to determine the following probabilities.
48. Four rainy days in a row when the forecast calls for a “20% chance of rain” each day
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
Chapter 7 Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Ch. 7.A - Suppose you toss one coin three times in a row and...Ch. 7.A - During the course of the basketball season, Shawna...Ch. 7.A - A box contains 20 chocolates, but only 2 of them...Ch. 7.A - Prob. 4QQCh. 7.A - When you toss one coin, the probability that...Ch. 7.A - On a roll of two dice, Serena bets that the sum...Ch. 7.A - Suppose you toss four 6-sided dice. How many...Ch. 7.A - Suppose you toss four 6-sided dice. How many...Ch. 7.A - You are playing 5-card poker with a deck of 52...Ch. 7.A - Prob. 10QQ
Ch. 7.A - Distinguish between an outcome and an event in...Ch. 7.A - 2. What does it mean when we write P(event)? What...Ch. 7.A - Briefly describe the differences among...Ch. 7.A - How is the probability of an event not occurring...Ch. 7.A - Prob. 5ECh. 7.A - Prob. 6ECh. 7.A - When I toss four coins, there are four different...Ch. 7.A - The probability that my sister will get into the...Ch. 7.A - I estimate that the probability of my getting...Ch. 7.A - Because either there is life on Mars or there is...Ch. 7.A - The probability that Jonas will win the race is...Ch. 7.A - Based on data showing that we’ve had snow on...Ch. 7.A - Prob. 13ECh. 7.A - 13-16: Review of the Multiplication Principle. Use...Ch. 7.A - Review of the Multiplication Principle. Use the...Ch. 7.A - Prob. 16ECh. 7.A - Prob. 17ECh. 7.A - Double-Header Outcomes and Events. Suppose the New...Ch. 7.A - Prob. 19ECh. 7.A - Prob. 20ECh. 7.A - Prob. 21ECh. 7.A - Prob. 22ECh. 7.A - Prob. 23ECh. 7.A - Prob. 24ECh. 7.A - 19-28: Theoretical Probabilities. Use the...Ch. 7.A - Theoretical Probabilities. Use the theoretical...Ch. 7.A - 19-28: Theoretical Probabilities. Use the...Ch. 7.A - 19-28: Theoretical Probabilities. Use the...Ch. 7.A - Prob. 29ECh. 7.A - Prob. 30ECh. 7.A - Prob. 31ECh. 7.A - Prob. 32ECh. 7.A - Which Type of Probability? State which method...Ch. 7.A - 33-34: Which Type of Probability? State which...Ch. 7.A - Prob. 35ECh. 7.A - Prob. 36ECh. 7.A - Event Not Occurring. Determine the probability of...Ch. 7.A - Prob. 38ECh. 7.A - Probability Distributions. Make a probability...Ch. 7.A - 39-42: Probability Distributions. Make a...Ch. 7.A - 39-42: Probability Distributions. Make a...Ch. 7.A - 39-42: Probability Distributions. Make a...Ch. 7.A - Prob. 43ECh. 7.A - Prob. 44ECh. 7.A - Prob. 45ECh. 7.A - Prob. 46ECh. 7.A - Prob. 47ECh. 7.A - Prob. 48ECh. 7.A - Prob. 49ECh. 7.A - Prob. 50ECh. 7.A - Prob. 51ECh. 7.A - Prob. 52ECh. 7.A - Prob. 53ECh. 7.A - Prob. 54ECh. 7.A - Computing Probabilities. Decide which method...Ch. 7.A - Computing Probabilities. Decide which method...Ch. 7.A - Prob. 57ECh. 7.A - Prob. 58ECh. 7.A - Prob. 59ECh. 7.A - Computing Probabilities. Decide which method...Ch. 7.A - Prob. 61ECh. 7.A - Prob. 62ECh. 7.A - Prob. 63ECh. 7.A - Prob. 64ECh. 7.A - Prob. 65ECh. 7.A - Prob. 66ECh. 7.A - Prob. 67ECh. 7.A - Probability Distributions 68.Suppose you have a...Ch. 7.A - Prob. 69ECh. 7.A - More Counting. Answer the following counting...Ch. 7.A - Prob. 71ECh. 7.A - Prob. 72ECh. 7.A - Prob. 73ECh. 7.A - Prob. 74ECh. 7.A - Senior Citizens. In 2010, there were 40 million...Ch. 7.A - Prob. 76ECh. 7.A - Prob. 77ECh. 7.A - Prob. 78ECh. 7.A - Prob. 79ECh. 7.A - Prob. 80ECh. 7.A - Prob. 81ECh. 7.A - Probability in the News. Find a news article or...Ch. 7.A - Prob. 83ECh. 7.A - Gambling Odds. Find an advertising for a gambling...Ch. 7.B - The probability of rolling two dice and getting a...Ch. 7.B - The rule PAandB=PAPBholdsa. in all cases.b. only...Ch. 7.B - Prob. 3QQCh. 7.B - A box of candy contains five dark chocolates and...Ch. 7.B - Prob. 5QQCh. 7.B - You roll two dice. Based on the probabilities...Ch. 7.B - You roll two dice twice. Based on the...Ch. 7.B - You toss two coins ten times, and you want to know...Ch. 7.B - Prob. 9QQCh. 7.B - Prob. 10QQCh. 7.B - How did the gambling habits of the Chevalier de...Ch. 7.B - 2. Give an example in which we would be interested...Ch. 7.B - 3. Give an example in which we would be interested...Ch. 7.B - 4. What is the at least once rule? Explain how the...Ch. 7.B - The probability of getting heads and tails when...Ch. 7.B - If you toss a corn and get heads three times in a...Ch. 7.B - The probability of drawing ace or a spade from a...Ch. 7.B - I can’t believe you chose the lottery number...Ch. 7.B - Prob. 9ECh. 7.B - To find the probability that at least one of my 25...Ch. 7.B - Chevalier’s Logic with Coins. The Chevalier’s...Ch. 7.B - Prob. 12ECh. 7.B - Prob. 13ECh. 7.B - Prob. 14ECh. 7.B - Prob. 15ECh. 7.B - Prob. 16ECh. 7.B - Prob. 17ECh. 7.B - Prob. 18ECh. 7.B - Prob. 19ECh. 7.B - Prob. 20ECh. 7.B - Prob. 21ECh. 7.B - Prob. 22ECh. 7.B - Prob. 23ECh. 7.B - 2 1-24: Either/Or Probabilities. Determine whether...Ch. 7.B - Prob. 25ECh. 7.B - 26. Randomly meeting three international students...Ch. 7.B - Prob. 27ECh. 7.B - Prob. 28ECh. 7.B - Prob. 29ECh. 7.B - Prob. 30ECh. 7.B - At Least Once Problems. Use the at least once rule...Ch. 7.B - Prob. 32ECh. 7.B - Prob. 33ECh. 7.B - Prob. 34ECh. 7.B - Prob. 35ECh. 7.B - Prob. 36ECh. 7.B - Prob. 37ECh. 7.B - Prob. 38ECh. 7.B - Prob. 39ECh. 7.B - Prob. 40ECh. 7.B - Prob. 41ECh. 7.B - Prob. 42ECh. 7.B - Prob. 43ECh. 7.B - Prob. 44ECh. 7.B - Prob. 45ECh. 7.B - Prob. 46ECh. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Prob. 49ECh. 7.B - Prob. 50ECh. 7.B - Prob. 51ECh. 7.B - Prob. 52ECh. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Prob. 54ECh. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Probability and Court. The data in the following...Ch. 7.B - Testing a Drug. A new cold medication was tested...Ch. 7.B - Prob. 59ECh. 7.B - Dominant and Recessive Genes. Many traits are...Ch. 7.B - Better Bet for the Chevalier. Suppose that the...Ch. 7.B - Prob. 62ECh. 7.B - Miami Hurricanes. Studies of the Florida...Ch. 7.B - Prob. 64ECh. 7.B - Prob. 65ECh. 7.B - Prob. 66ECh. 7.B - Prob. 67ECh. 7.B - Combined Probability in Your Life. Cite a recent...Ch. 7.C - Suppose that the probability of a hurricane...Ch. 7.C - Consider a lottery with 100 million tickets in...Ch. 7.C - Consider the lottery described in Exercise 2. If...Ch. 7.C - Prob. 4QQCh. 7.C - An insurance company knows that the average cost...Ch. 7.C - You know a shortcut to work that uses side streets...Ch. 7.C - Cameron is betting on a game in which the...Ch. 7.C - Prob. 8QQCh. 7.C - A $1 slot at a casino is set so that it returns...Ch. 7.C - Consider the slot machine described in Exercise 9....Ch. 7.C - Explain the meaning of the law of large numbers....Ch. 7.C - In 10 tosses of a fair coin, should you be...Ch. 7.C - Prob. 3ECh. 7.C - Prob. 4ECh. 7.C - Prob. 5ECh. 7.C - Prob. 6ECh. 7.C - The expected value to me of each raffle ticket I...Ch. 7.C - The expected value of each insurance policy our...Ch. 7.C - If you toss a coin four times, it’s much more...Ch. 7.C - I haven’t won in my last 25 pulls on the slot...Ch. 7.C - I haven’t won in my last 25 pulls on the slot...Ch. 7.C - I’ve lost S750 so far today on roulette. I’m going...Ch. 7.C - Understanding the Law of Large Numbers. Suppose...Ch. 7.C - Speedy Driver. Suppose a person who has a habit of...Ch. 7.C - Prob. 15ECh. 7.C - Expected Value Games. Find the expected value (to...Ch. 7.C - Prob. 17ECh. 7.C - Expected Value Games. Find the expected value (to...Ch. 7.C - Prob. 19ECh. 7.C - Prob. 20ECh. 7.C - Prob. 21ECh. 7.C - Expected Wait. A bus arrives at a bus stop at...Ch. 7.C - Gambler’s Fallacy and Coins. Suppose you play a...Ch. 7.C - Gambler’s Fallacy and Dice. Suppose you roll a die...Ch. 7.C - Can You Catch Up? Suppose you toss a fair coin 100...Ch. 7.C - Prob. 26ECh. 7.C - Prob. 27ECh. 7.C - Prob. 28ECh. 7.C - Prob. 29ECh. 7.C - Prob. 30ECh. 7.C - Prob. 31ECh. 7.C - Prob. 32ECh. 7.C - Prob. 33ECh. 7.C - Prob. 34ECh. 7.C - Extra Points in Football. Football teams have the...Ch. 7.C - Roulette. When you bet $5 on the number 7 in...Ch. 7.C - Household Size. It is estimated that 57% of...Ch. 7.C - Prob. 38ECh. 7.C - Prob. 39ECh. 7.C - Prob. 40ECh. 7.C - Prob. 41ECh. 7.C - The Morality of Gambling. Republican Senator...Ch. 7.D - Prob. 1QQCh. 7.D - Prob. 2QQCh. 7.D - Prob. 3QQCh. 7.D - Prob. 4QQCh. 7.D - Prob. 5QQCh. 7.D - Based on Figure 7.11, besides the elderly, the...Ch. 7.D - Prob. 7QQCh. 7.D - Prob. 8QQCh. 7.D - Based on Figure 7.12, which statement is not...Ch. 7.D - Prob. 10QQCh. 7.D - Prob. 1ECh. 7.D - Prob. 2ECh. 7.D - Prob. 3ECh. 7.D - Prob. 4ECh. 7.D - Prob. 5ECh. 7.D - Prob. 6ECh. 7.D - Your life expectancy is the major factor in...Ch. 7.D - A 60-year-old has a shorter life expectancy than...Ch. 7.D - Prob. 9ECh. 7.D - Prob. 10ECh. 7.D - Prob. 11ECh. 7.D - Prob. 12ECh. 7.D - Prob. 13ECh. 7.D - Prob. 14ECh. 7.D - Prob. 15ECh. 7.D - 15–20: Causes of Death. Use Table 7.4, and assume...Ch. 7.D - Prob. 17ECh. 7.D - Prob. 18ECh. 7.D - 15–20: Causes of Death. Use Table 7.4, and assume...Ch. 7.D - 15–20: Causes of Death. Use Table 7.4, and assume...Ch. 7.D - Prob. 21ECh. 7.D - Prob. 22ECh. 7.D - Prob. 23ECh. 7.D - Prob. 24ECh. 7.D - Prob. 25ECh. 7.D - Prob. 26ECh. 7.D - Prob. 27ECh. 7.D - Prob. 28ECh. 7.D - Prob. 29ECh. 7.D - Prob. 30ECh. 7.D - Prob. 31ECh. 7.D - Prob. 32ECh. 7.D - Prob. 33ECh. 7.D - Aging population. The table shows the U S....Ch. 7.D - Prob. 35ECh. 7.D - Prob. 36ECh. 7.D - Prob. 37ECh. 7.D - Prob. 38ECh. 7.D - Prob. 39ECh. 7.E - 1. You are asked to create a 4-character password,...Ch. 7.E - Prob. 2QQCh. 7.E - A teacher has 28 students. and 5 them will be...Ch. 7.E - Prob. 4QQCh. 7.E - A soccer coach who has 15 children on her team...Ch. 7.E - One term in the denominator of the combinations...Ch. 7.E - Overall, number of different 4-person terns (order...Ch. 7.E - One in a stadium filled with 100,000 people is...Ch. 7.E - One in a stadium filled With people is chosen at...Ch. 7.E - There are 365 possible birthdays in a year. In a...Ch. 7.E - Prob. 1ECh. 7.E - Prob. 2ECh. 7.E - Prob. 3ECh. 7.E - 4. Explain What we mean When we that outcome is...Ch. 7.E - I used the permutations formula to determine how...Ch. 7.E - I used the combinations formula to determine how...Ch. 7.E - The number Of different possible batting orders...Ch. 7.E - It must my lucky day, the five-card poker hand I...Ch. 7.E - The probability that two people in a randomly...Ch. 7.E - Someone wins the lottery every week. so I figure...Ch. 7.E - Review of Factorials. use the skills covered in...Ch. 7.E - Review of Factorials. use the skills covered in...Ch. 7.E - Review of Factorials. use the skills covered in...Ch. 7.E - Prob. 14ECh. 7.E - Prob. 15ECh. 7.E - Prob. 16ECh. 7.E - Prob. 17ECh. 7.E - Prob. 18ECh. 7.E - Review off Factorials. use the skills covered in...Ch. 7.E - 11—22: Review off Factorials. use the skills...Ch. 7.E - 11—22: Review off Factorials. use the skills...Ch. 7.E - 11—22: Review off Factorials. use the skills...Ch. 7.E - Prob. 23ECh. 7.E - Counting Methods. Answer the following questions...Ch. 7.E - Prob. 25ECh. 7.E - Prob. 26ECh. 7.E - Prob. 27ECh. 7.E - Prob. 28ECh. 7.E - Prob. 29ECh. 7.E - Prob. 30ECh. 7.E - Prob. 31ECh. 7.E - Prob. 32ECh. 7.E - Counting Methods. Answer the following questions...Ch. 7.E - Prob. 34ECh. 7.E - Prob. 35ECh. 7.E - Prob. 36ECh. 7.E - Prob. 37ECh. 7.E - Prob. 38ECh. 7.E - Prob. 39ECh. 7.E - Prob. 40ECh. 7.E - Birthday Coincidences. Suppose you are part of a...Ch. 7.E - Birthday Coincidences. Suppose you are part of a...Ch. 7.E - 43. Ice Cream Shop. Josh and Ice Cream Shop Of-...Ch. 7.E - 44. Telephone Numbers. A ten-digit phone number in...Ch. 7.E - 45. Pizza Hype. Luigi; Pizza parlor advertises 56...Ch. 7.E - ZIP Codes. The US. Postal Service five-digit and...Ch. 7.E - 47 —54: Counting and Probability. Find the...Ch. 7.E - Prob. 48ECh. 7.E - Prob. 49ECh. 7.E - Prob. 50ECh. 7.E - Prob. 51ECh. 7.E - Prob. 52ECh. 7.E - Prob. 53ECh. 7.E - Prob. 54ECh. 7.E - Hot Streaks. Suppose that 2000 people are all...Ch. 7.E - Joe Record. One of longest-standing records in...Ch. 7.E - Prob. 57ECh. 7.E - Prob. 58ECh. 7.E - Prob. 59ECh. 7.E - Prob. 60ECh. 7.E - Prob. 61ECh. 7.E - Prob. 62ECh. 7.E - Prob. 63ECh. 7.E - Prob. 64E
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