6. Someone plans to travel at the weekend. According to the weather forecast, the probability ofraining on the first and the second day of weekends is 0.5 and 0.3 respectively, the probability ofraining on both days is 0.2. Try to find:(Let Ai be event of raining on the ith day, i = 1,2, then P (A₁) = 0.5, P (A2) = 0.3, P (A1 A2) = 0.2.)(1) The probability of raining on the first day but not on the second day;(2) The probability of raining on one of the two days;(3) The probability of raining at least on one day.

1) To find the probability of raining on the first day but not on the second day, we can use the…

Answered: 6. Someone plans to travel at the…

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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The probability that a student will pass in the Economics test is 2/3, and that a vill not pass in the English test is 5/9. If the probability of his passing in at ne ane of these two tests is 4/5 , find the probability that he will pass in both 20 is the tests. CS Scanned with CamScanner
Suppose E= "sum is 5" and F= "exactly one of the dice is even". Are E and F independent? Explain why or why not.
A class contains 40 students. The probability of failing in one of the courses for each student is 0.03, but there is no chance to fail in more than one course. You know that a student failed in a course, the probability that the fail reason in non-attendance is 0.04. All other fail reasons are low average. The examinations are private, so the results are mutually independent. Let X and Y be the numbers of failed students due to non-attendance and due to low average, respectively, in that class this semester. Find the joint MGF
Suppose that in a year of 365 days, it rains on 62 days. There is lightning on 13 days. There is both lightning and rain on 12 days. Compare the chance that a rainy day has lightning to the chance that a day with lightning has rain. Show your work here P(lightning | rain) = P(rain | lightning)
The probability of afternoon rain given morning cloud cover >50% is of interest to those forecasting the weather. You can calculate this probability using Bayes' Theorem (below). The probability of morning cloud cover in general is 30% in the area you are concerned with and when there's afternoon rain, morning cloud cover of the kind described above occurs 90% of the time. The probability of rain in general for the area is about 26% of days. From the above information, identify what P(BIA) would be. Express your answer as a proportion, rounded to two decimal places. P(A/B)= = P(B|A)*P(A) P(B)
Assume that three stop lights on the way to school are independent. Their time probabilities are P(Red)=0.4, P(Green)=0.5, and P(Yellow)=0.1 values. What is the probability of getting ALL THREE green lights on a trip to school?
Answers must be in 4 decimals 1. The probability that IEntelligent will open a review center in Quezon City is 0.7, the probability that is will open a review center in Laguna is 0.4, and the probability that it will open a review center in either QC or Laguna or both is 0.8. what is the probability that IEntelligent will locate in both locations? 2. The probability that IEntelligent will open a review center in Quezon city is 0.7, the probability that is will open a review center in Laguna is 0.4, and the probability that it will open a review center in either QC or Laguna or both is 0.8. What is the probability that IEntelligent will locate in QC only?
A student in this class is writing two midterms in math this week. The probability that she will pass MAT 2371 is 0.7, and the probability that she will pass MAT 2125 is 0.7. If the result on the two exams are independent, what is the probability that she will fail at least one the two exams? 0.56 0.44 0.54 0.46 0.51
The device consists of 3 elements. The probability of failure free operation of each of them are respectively equal to. 0.6, 0.7, 0.8. Find the probability that at least two of elements will work without fail.
Q. 2 The probability that a smoker who consumes over 20 cigarettes a day will suffer from chronic respiratory illness is 4 The 10 probability that he will suffer from heart disease is The 10 probability that he will suffer from at least one of these ailments is 6.5 10 (i) Find the probability that the smoker will suffer from both ailments. (ii) Find the probability that he will suffer from heart disease given that he suffers from chronic respiratory illness. (iii) Find the probability that he will suffer from chronic respiratory illness given that he suffers from heart disease. (iv) Are events "chronic respiratory illness" and "heart disease independent"?
Please provide steps for how you got the solution to the problem provided below. A machine is used to produce one of each of two types of product (A and B) on alternating days, i.e., if A is produced today then B will be produced tomorrow and vice versa. Each day, there is a probability that the machine malfunctions. Malfunction probability after a day of operation is 0.03 when producing A and 0.07 when producing B. Once the machine malfunctions, it is no longer operable and will not be replaced until sometime in the future (beyond modeling horizon). Model the system as a Markov chain (give transition matrix on your paper). Suppose that on Monday product A was produced. Find the probability that the machine is still operable by the morning of Thursday. Your model should have a state ”malfunction”, which cannot transition to any other state other than itself.
Suppose the probability of getting the flu is 0.20, the probability of getting a flu shot is 0.60, and the probability of bothgetting the flu and a flu shot is 0.10. (a) Find the probability of the union between (getting the the flu) and (getting the flu shot).

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