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?

Given that, the route used by a certain motorist in commuting to work contains two intersections…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Imagine a man has two emotional type for each day: Happy and Sad. If he is happy in one day, then the probability of being happy in the next day is 0.8, while the probability of being sad is 0.2; if he is sad in one day, the probability of being sad is 0.6 and being happy at 0.4. (a) If he is happy today. What is the probability that he is happy tomorrow? (b) If he is happy today. What is the probability that he is happy the day after tomorrow? (c) If he is happy today. Given that he is happy the day after tomorrow, what is the probability that he is happy tomorrow?
An engineering graduate applies for a job in two firms $X$ and Y$ The probability that he is selected in the firm X is 0.7 and being rejected at Y is 0.4. The probability of at leastone of his applications being rejected is 0.4. What is the probability that he will be selected in one of thefirms?
(ii) At a Harford university, the probability that a student takes calculus and agriculture in the same semester is 0.09. The probability that a student takes agriculture is 0.15. The probability that a student takes calculus is 0.6. a. State, giving a reason in each case whether probability of calculus and probability of agriculture are independent b. Find the probability that a student is taking calculus, given that he or she is taking agriculture.
An examination consists of two papers , Paper 1 and Paper 2 . The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2 . Given that a student has failed in Paper 2 , the probability of failing in Paper 1 is 0.6 . Then the probability of a student failing in both the papers is equal to
When Mitchell drives back home from campus, he has to pass through two sets of traffic lights. The probability that he has to stop at the first is 0.33, while the probability he has to stop at the second set is 0.41. Also, the probability he does not have to stop at either traffic light is 0.31. What is the probability he has to stop at exactly one set of traffic lights?
The probability of a thunderstorm on Memorial Day is 0.13 and the probability of a thunderstorm on Independence Day is 0.59. Assuming that these two are Independent, what is the probability of thunderstorms on both Memorial and Independence Day?
For this problem, assume that you weigh 500 duck hatchlings. You find that 93 are slightly underweight, 6 are severely underweight, and the rest are normal. (1) What probability should be assigned to a single duck hatchling's being slightly underweight? (2) What probability should be assigned to a single duck hatchling's being severely underweight? (3) What probability should be assigned to a single duck hatchling's being normal?
The problem of traffic delay in a highway can be studied in the following way. Let us assume that the probability of no traffic delay in one period, given no traffic delay in previous period, is 0.85 and that the probability of finding a traffic delay in one period, given a delay in the previous period is 0.75. The period of time is 30 minutes.
If the probability of one event occurring is 1/4 and the probability of another event occurring is 1/10, what is the probability that both events will occur?
For this problem, assume that 11 % withdraw, 14 % receive an A, 18 % receive a B, 35 % receive a C, 14 % receive a D, and 8 % receive an F. (1) What probability should be assigned to the event "pass the course"? (2) What probability should be assigned to the event "withdraw or fail the course"?
A BSCE student is taking Calculus 2 and Engineering Data Analysis courses. The probability that he will pass Calculus 2 and Engineering Data Analysis is 2/3and 4/9, respectively. What is the probability that he will pass both courses if the probability of passing at least one course is 4/5.
A study tracked a large group of people for 10 years. At the start of the study, 20% were heavy smokers (H), 30% were light smokers (L), and 50% were non-smokers (N). The interest of the study was whether the people in the study died during the study (D) or not die (Dc ). The probability that a light smoker died during the study was twice that of the probability of a non-smoker dying. Also, the probability that light smoker died during the study was half that of the probability of a heavy smoker dying. A randomly selected person from the study died during the study. What is the probability that this person was a heavy smoker (given they died, what is the probability they were a heavy smoker H)?

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