1 Linear Equations And Straight Lines 2 Matrices 3 Linear Programming, A Geometric Approach 4 The Simplex Method 5 Sets And Counting 6 Probability 7 Probability And Statistics 8 Markov Processes 9 The Theory Of Games 10 The Mathematics Of Finance 11 Logic 12 Difference Equations And Mathematical Models expand_more
6.1 Experiments, Outcomes, Sample Spaces, And Events 6.2 Assignment Of Probabilities 6.3 Calculating Probabilities Of Events 6.4 Conditional Probability And Independence 6.5 Tree Diagrams 6.6 Bayes’ Theorem, Natural Frequencies 6.7 Simulation Chapter Questions expand_more
Problem 1CYU: 1. Cards Suppose that there are three cards: one red on both sides; one white on both sides; and one... Problem 2CYU: Show that if events E and F are independent of each other, then so are E and F'. [Hint: Since... Problem 1E: 1. The Venn diagram in Fig. 3 shows the probabilities for its four basic regions. Find
Figure... Problem 2E: 2. The Venn diagram in Fig. 4 shows the probabilities for its four basic regions. Find
Figure... Problem 3E: Let S be a sample space and E and F be events associated with S. Suppose that... Problem 4E: Let S be a sample space and E and F be events associated with S. Suppose that... Problem 5E: Let S be a sample space and E and F be events associated with S. Suppose that... Problem 6E: 6. Let S be a sample space and E and F be events associated with S. Suppose that .... Problem 7E: Let S be a sample space and E and F be events associated with. Suppose that... Problem 8E: Let S be a sample space and E and F be events associated with S. Suppose that... Problem 9E: Dice When a pair of dice is rolled, what is the probability that the sum of the dice is 8, given... Problem 10E: 10. Dice When a pair of dice is rolled, what is the probability that the sum of the dice is 5, given... Problem 11E: Coins A coin is tossed three times. What is the probability that the outcome is three heads, given... Problem 12E: Coins A coin is tossed three times. What is the probability that the outcome contains no heads,... Problem 13E: Bag of Marbles A bag contains five red marbles and seven white marbles. If a sample of four marbles... Problem 14E: Balls in an Urn Two balls are selected at random from an urn containing two white balls and three... Problem 15E: 15. Children Suppose a family has two children and the youngest is a girl. What is the probability... Problem 16E: Children Suppose a family has two children and at least one is a girl. What is the probability that... Problem 17E: 17. Value of College Twenty-five percent of individuals in a certain city earn more than $45,000 per... Problem 18E: Advanced Degrees Sixty percent of the teachers at a certain high school are female. Forty percent of... Problem 19E: Advanced Degrees Table 1 shows the projected number of advanced degrees (in thousands) earned in the... Problem 20E: 20. Voting Table 2 shows the number of registered voting-age U.S. citizens (in millions) by gender... Problem 21E: Military Personnel Table 3 shows the numbers (in thousands) of officers and enlisted persons on... Problem 22E: 22. College Majors Table 4 shows the probable field of study for 1500 freshman males and 1000... Problem 23E: 23. Bills in Envelopes Each of three sealed opaque envelopes contains two bills. One envelope... Problem 24E: 24. Gold and Silver Coins Consider three boxes. One box contains two gold coins, one box contains... Problem 25E: 25. Cards A sequence of two playing cards is drawn at random (without replacement) from a standard... Problem 26E: Cards A sequence of two playing cards is drawn at random (without replacement) from a standard deck... Problem 27E: Coin Tosses A coin is tossed five times. What is the probability that heads appears on every toss,... Problem 28E: Coin Tosses A coin is tossed twice. What is the probability that heads appeared on the first toss,... Problem 29E: 29. Exit Polling According to exit polling for the 2016 Missouri Republican primary election, 48% of... Problem 30E: Population Twenty percent of the worlds population live in China. The residents of Shanghai... Problem 31E: 31. Basketball Suppose that your team is behind by two points and you have the ball on your... Problem 32E: 32. Password Fred remembers all but the last character of the password for his e-mail account.... Problem 33E: Let E and F be events with P(E)=.4,Pr(F)=.5, and Pr(EF)=.7. Are E and F independent events? Problem 34E: 34. Let E and F be events with , and. Are E and F independent events?
Problem 35E: 35. Let E and F be independent events with . Find .
Problem 36E: 36. Let E and F be independent events with and . Find .
Problem 37E: In Exercises 3740, assume that E and F are independent events. Use the given information to find... Problem 38E: In Exercises 3740, assume that E and F are independent events. Use the given information to find... Problem 39E: In Exercises 37–40, assume that E and F are independent events. Use the given information to find... Problem 40E: In Exercises 3740, assume that E and F are independent events. Use the given information to find... Problem 41E: Let A, B, and C be independent events with Pr(A)=.4,Pr(B)=.1,andPr(C)=.2. Calculate Pr[(ABC)]. Problem 42E: 42. Let A, B, and C be independent events with , and . .
Problem 43E: 43. Balls in an Urn A sample of two balls is drawn from an urn containing two white balls and three... Problem 44E: Balls in an Urn An urn contains two white balls and three red balls. A ball is withdrawn at random... Problem 45E: 45. Roll a Die Roll a die, and consider the following two events: . Are the events E and F... Problem 46E: Roll a Die Roll a die, and consider the following two events: E={2,4,6},F={3,4,6}. Are the events E... Problem 47E: Rolling Dice Roll a pair of dice, and consider the sum of the two numbers. Are the events the sum is... Problem 48E: Rolling Dice Roll a pair of dice, and consider the sum of the two numbers. Are the events the sum is... Problem 49E: 49. Epidemiology A doctor studies the known cancer patients in a certain town. The probability that... Problem 50E: 50. Blood Tests A hospital uses two tests to classify blood. Every blood sample is subjected to both... Problem 51E: Medical Screening A medical screening program administers three independent tests. Of the persons... Problem 52E: Guessing on an Exam A truefalse exam has 10 questions. Assuming that the questions are independent... Problem 53E: 53. System Reliability A TV set contains five circuit boards of type A, five of type B, and three of... Problem 54E: System Reliability In November 2015, Intel announced the release of a business desktop computer with... Problem 55E: 55. Smartphones Suppose that in Sleepy Valley, 70% of those over 50 years old own smartphones. Find... Problem 56E: 56. Fishing The probability that a fisherman catches a tuna in any one excursion is .15. What is the... Problem 57E: Baseball A baseball players batting average changes every time he goes to bat and therefore should... Problem 58E: Roulette If you bet on the number 7 in roulette, the probability of winning on a single spin of the... Problem 59E: Free-Throws A basketball player makes each free-throw with a probability of .6 and is on the line... Problem 60E: 60. Free-Throws Rework Exercise 59 with a probability of .7.
Problem 61E: Free-Throws Consider Exercise 59, but let the probability of success be p, where 0p1. Explain why... Problem 62E: Free-Throws Consider Exercise 59, but let the probability of success be p, where 0p1. For what value... Problem 63E Problem 64E: 64. Coin Toss A coin is tossed five times. Is the outcome HTHHT more likely to occur than the... Problem 65E Problem 66E Problem 67E Problem 68E: 68. Use the inclusion–exclusion principle for (nonconditional) probabilities to show that, if E, F,... Problem 69E Problem 70E format_list_bulleted