[Probability] Two friends come into a same coffee place on a regular basis. Every day each friendstops by at the coffee place between 2pm and 3pm, but at random moments of time (uniformlydistributed across the given hour) and independently from each other. Each stays in the cafe forexactly 20 minutes. What is the probability that two friends meet at the cafe on a given day(assuming a meeting occurs with certainty if they both are there at the same moment of time)?

The time at which friends stop by at the coffee place is between pm and pm.They stop there at…

Answered: [Probability] Two friends come into a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light. Traffic light A Traffic light B Traffic light C ?(?) ?(?) ?(?) 0.4 0.6 0.7 What is the probability that the employee is not late for work? Please write your answer in decimal form, rounded to three decimal places.
Events A and B are mutually exclusive. Suppose event A occurs with probability 0.48 and event B occurs with probability 0.42. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that A does not occur or B does not occur (or both). (b) Compute the probability that either B occurs without A occurring or A and B both occur.
Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light. Traffic light A Traffic light B Traffic light C ?(?)P⁡(A) ?(?)P⁡(B) ?(?)P⁡(C) 0.6 0.4 0.9 What is the probability that the employee is not late for work? (Round to 3 decimal places)
Two students are registered for the same class and attend independently of each other, student A 80% of the time and student B 70% of the time. The teacher remembers that on a given day at least one of them is in class. What is the probability that student A was in class that day? (Round your answer to three decimal places.)
In a certain population of people, 72% of the people have brown eyes and 28% of the people have blue eyes. What is the probability that two randomly selected people (not related to each other) from this population will have eyes of the same color? (Answer correctly to 3 decimal places.)
Find the probability that when a couple has five children, at least one of them is a girl. (Assume that boys and girls are equally likely.) The probability is ? that at least one of the five children is a girl.
The three-year recidivism rate of parolees in a certain state is about 20%; that is, 20% of parolees end up back in prison within three years. Assume that whether one parolee returns to prison is independent of whether any of the others return. Complete parts a and b below. Find the probability that exactly 6 out of 20 parolees will end up back in prison within three years. The probability that exactly 6 out of 20 parolees will end up back in prison is nothing.
On any given day, a certain machine has either no malfunctions or exactly one malfunction. The probability of malfunction on any given day is 0.40. Machine malfunctions on different days are mutually independent. Calculate the probability that the machine has its third malfunction on the fifth day, given that the machine has not had three malfunctions in the first three days.
On any given morning here at Chabot College, coffee is brewed in the Science and Math Division workroom by one of two faculty members, depending on who arrives first at work. Instructor Yest arrives first 75% of the time. Instructor Kelly arrives first the remaining mornings. The probability that the coffee is brewed strong when brewed by Instructor Yest is 0.2. The probability that the coffee is brewed strong when brewed by Instructor Kelly is 0.9, as Instructor Kelly likes her coffee strong! Given the coffee is strong on a randomly selected morning, what is the probability that is was brewed by Instructor Yest?
Let A and B be two events such that the probability of B is 0.5 and the probability of both is 0.2. Find the probability of A given that B occurs.
An airline claims that there is a 0.10 probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight. This outcome is independent from flight to flight. Sam is a frequent flier who always purchases coach-class tickets. What is the probability that Sam’s first upgrade will occur after the third flight? What is the probability that Sam will be upgraded exactly 2 times in his next 20 flights? Sam will take 104 flights next year. Would you be surprised if Sam receives more than 20 upgrades to first class during the year? Justify your answer.
Suppose the probability of a customer placing an order at a pizza place for a pepperoni pizza is 0.6, and for something else with probability 0.4. We assume if a customer calls the pizza place, he orders something, and that all incoming calls are indepen- dent. What is the probability that the pizza place will get the first pepperoni pizza order on the 4th call of the day?

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