On average, an office receives a phone call every 5 minutes. For each call, the two operators, and Bob flip a fair coin to decide who takes the call. (a) Calculate the probability that exactly two calls arrive between 10:00 and 10:20. (b) Calculate the probability that between 10:00 and 10:20, all calls are taken by Alice. (c) Assuming that between 10:00 and 10:20, 3 calls arrive in total, what is the conditional proba- bility that Alice has taken exactly two of those calls?

On average, an office receives a phone call every 5 minutes. For each call, the two operators, and Bob flip a fair coin to decide who takes the call. (a) Calculate the probability that exactly two calls arrive between 10:00 and 10:20. (b) Calculate the probability that between 10:00 and 10:20, all calls are taken by Alice. (c) Assuming that between 10:00 and 10:20, 3 calls arrive in total, what is the conditional proba- bility that Alice has taken exactly two of those calls?

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...

See similar textbooks

Similar questions

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)
A city has two daily newspapers, A and B. A survey of 100 residents of the city shows that 35 people subscribe to A, 60 subscribe to B and 20 subscribe to both. Find the probability that a resident chosen is subscribing to A only?
Please solve all parts of 8.51
Assume that 2 cards are drawn in succession and without replacement from a standard deck of 52 cards. Find the probability that the following occurs. (Enter your probability as a fraction.) The second card is a king, given that the first card was a king.
The probability that the first record of a singing group will be a hit is 0.48. If their first record is a hit, so are all their subsequent records. If their first record is not a hit, the probability of their second and all subsequent ones being hits is 0.24. If the first two records are not hits, the probability that the third is a hit is 0.12. Find the probability that a group has exactly 2 hits in their first three records. P(exactly 2 hits in first three records) = (Simplify your answer. Type an integer or a decimal. Round to 6 places.)
A hacker is trying to guess someone's password.The hacker knows that the password is 4 digits long,and that each digit could be a number between 0 and 3.Assume that the hacker makes random guesses.What is the probability that the hacker guesses the password right on her first try?
Each of the numbers 0 - 9 is written on a sheet of paper and the ten sheets of paper are placed in a box If two of these sheets of paper are selected from the box at random, without replacement, find the probability that both numbers are greater than 7.
There are two urns, one containing a blue sock and the other a red sock. A person randomly picks a sock. After this, someone puts a red sock in the empty urn. The person again randomly picks a sock and it is the probability that the first sock was red?
A certain disease has a prevalence of in a population. The rate of false 4 positives is 10% and and the rate of false negatives is 5%. If you are exposed to the disease, then probability that you contract it is . You can only contract the disease by sharing food. Suppose that you meet 10 people, that each person tests negative for the disease, and that you share food with each of them exactly three times. What is the probability that you contract the disease?
Jack has just been given a ten-question multiple choice quiz in history class. Each question has five answers, of which only one is correct. Since Jack has not attended class recently, he does not know any of the answers. Assuming Jack guesses randomly on all ten questions, find the probability that he will answer six or more of the questions correctly and avoid an F.
Two cards are drawn at random and replaced after each draw. Given that the first card was a Jack of Hearts, find the probability that the second card was a diamond.