where the first outcome is one of X, Y, and Z, and the second outcome in each case is one of A and B. Use the following probabilities instead of those given in your text: Pr[X]=37 Pr[Y]=27 Pr[Z]=27 Pr[A|X]=45 Pr[B|X]=15 Pr[A|Y]=23 Pr[B|Y]=13 Pr[A|Z]=18 Pr[B|Z]=78 Pr[(XorY)|B]=

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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If P (A) = 0.6, P (B) =0.5 and P (A U B) = 0.9, find the following probabilities: (a) P (ANB) (b) P (A/B)
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Suppose you are deciding whether or not to bring an umbrella to school and the weathercan be either sunny or rainy. Initially, you think the probability that it will be sunny isP (S) = 0.6, and the probability that it will be rainy is P (R) = 0.4. If you bring an umbrellaand it rains, your payoff is 6. If you bring an umbrella and it is sunny, your payoff is 9. Ifyou don’t bring an umbrella and it rains, your payoff is 0. If you don’t bring an umbrellaand it is sunny, your payoff is 10. Suppose that you check two websites for weather forecasts.You know that the two forecasts are independent of each other, and each forecast is correct70% of the time. That is, the probability that the website says it will be sunny given that itactually will be sunny is 0.7, and the probability that the website says it will rain given thatit actually will rain is 0.7. Suppose that you suffer from confirmation bias. You initially thinkit is more likely to be sunny, so you misinterpret rain forecasts as sun…
In a town, there are three bridges: Bridge A, Bridge B, and Bridge C. On any given day, the probability of each bridge being open for passage is as follows: P(A) = 0.4, P(B) = 0.3, and P(C) = 0.5. If a resident needs to cross all three bridges in succession, what is the probability of successfully crossing all three bridges without encountering any closures?
The probability of an integrated circuit passing a quality test is F. In a batch of 10 integrated circuits find the probabilities thati. 2 will failii. 8 will passiii. at least 2 will failiv. fewer than 2 will fail.
Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here. O 0.159 O 0,259 0 0.448 O 0,741 Save and Exit Next Submit Math and rem 96 & 7 8 9. 10
Sarah and Thomas are going bowling. The probability that Sarah scores more than 175 is 0.5 , and the probability that Thomas scores more than 175 is 0.1 . Their scores are independent. Round your answers to four decimal places, if necessary. (a) Find the probability that both score more than 175 . (b) Given that Thomas scores more than 175 , the probability that Sarah scores higher than Thomas is 0.4 . Find the probability that Thomas scores more than 175 and Sarah scores higher than Thomas.
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?
Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have. P(x) ХP(x) 0.15 1 0.25 0.35 4 0.10 0.05 6 (or more) 0.05 (a) Find the probability that a married adult has three children. (Enter your answer to two decimal places.) (b) In words, what does the expected value in this example represent? O the average number of children married adults in the country have the average number of children adults in the country have O the number of children married adults in the country have O the number of children adults in the country have (c) Find the expected value. (Enter your answer to two decimal place.) children (d) Is it more likely that a married adult will have two to three children or four to six children? How do you know? O it is more likely to have two to three children, with p = 0.35 O it is more likely to have four…
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P(A)=0.55,P(B)=0.58,P(B∪A)=0.86 Find the following probabilities. P(A∩B) = P(B|A) = P(A|B) =