Suppose again that the lifetime of a particular model of laptop is exponentiallydistributed with a mean of 4 years. Suppose you bought a laptop one year ago and like it somuch that you buy a second one of the same model for a friend (spouse, sibling, etc.).a) What is the probability that your laptop outlasts the laptop you bought for your friend?b) What is the expected time until one of the laptops fails?

Let X be the random variable representing the lifetime of the considered laptop in years. The…

Answered: Suppose again that the lifetime of a…

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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(7) If the probability of a student graduating is 0.95, find the probability that more than 472 students students graduating among 500 students.
The Hurricane Science Society is attempting to gather information about upcoming hurricanes. Due to climate change, scientists are predicting that more attention will be turned toward natural disasters in the future.The mean number of hurricanes to hit Florida per year is 0.8 over the last 50 years. (a) Calculate the probability that 1 hurricane will hit Florida (b) Calculate the probability that at most 2 hurricanes will hit Florida.(c) Calculate the probability that more than 3 hurricanes will hit Florida.
Suppose that 70% of all students in a large university pass all their classes. Find the probability that more than 60% of 34 r/s students from this university pass all their classes.
It has rained for 18 days out of the last 30. Using this information, what is the likelihood that it will rain tomorrow?
The probability of a 25-year-old and another 35-year-old living together for 10 years is 0.6. What is the probability that a 30-year-old person will die within 15 years, if it is known that 4000 people out of 54000 at 25 years old will die before reaching the age of 30?
What is the probability that the total of two randomly chosen numbers exceeds 3, where the first number is chosen from a uniform distribution between 0 and 2, and the second number is selected from an exponential distribution with a mean of 1?
A bag contains 2 red balls worth £3, 2 blue balls worth £2 and 5 green balls worth £0. You pick 1 ball out of the bag (without replacement). What the expected value of earnings from playing this game once (3 decimal places).
Q3 a) A component has an exponential time to failure with a mean of 100 hours. (i) The component has already been in operation for its mean life. What is the probability that it will fall by 150 hours? (ii) The component will operate for another 50 hours given that it is in operation 150 hours. (iii) If 20 components are tested, what is the probability that at least one fails in less than 200 hours? Assume that the components fail independently. b) Students of National University were classified according to their favorite color: Blue 12 5 Favorite color Red 13 13 Black 25 20 Male Female If one student is selected at random, then find the probability that the selected student: (i) Doesn't like black color. (ii) Is Female and likes blue color. (iii) Is Male or like black color. (iv) Likes red color given that it is female.
The mosquitos are out in your back yard, and they bite you at random times. Each bite happens independently of the last bite. The average time between bites is 2.501 minutes. What is the probability that it takes longer than 1 minutes for them to first bite you?
If 15% of adults in a certain country work from home, what is the probability that fewer than 30 out of a random sample of 250 adults will work from home? (Round your answer to 3 decimal places)
Suppose that the lifetime of a soft white light bulb follows an exponential distribution with expected value 300 hours, and the lifetime of an bright white light bulb follows an exponential distribution with expected value 700 hours, and the two lifetimes are independent. If we start using both light bulbs at the same time, then what is the probability that the soft white light bulb will burn out before the bright white light bulb?
In a 24-hour call center, complaints arrive at a mean rate of 1 complaint every 3 hours. (a) Find the probability that there are at most 3 complaints in the past 10 hours. (b) A day is “doomed” if there are at least 6 complaints. Each day, an inspector counts the number of complaints at the end of the day and determines whether the day was doomed. Find the probability that the inspector has worked for 7 days when he records the 3rd doomed day. (c) Find the probability that there are at least 2 complaints in the past 12 hours given that there are at most 5 complaints in the past 12 hours

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