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

Player A and Player B play chess (either of them wins, a draw is not permitted). If player A plays White, the probability of him/her winning is 0.72. If player A plays Black, the probability of him/her winning is 0.63. Player A and Player B play 2 games and in the second game, they change sides. Find the probability that player B wins both games.
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?
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?
A box (Call it Box A) contains four red marbles and three blue marbles. Box B (another box) contains three red and three blue marbles. Find the probability that, when a marble is drawn from each box (a) Both are red (b) One is red and the other is blue
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?
The digits 2, 3, 4, 5, 6, 7, and 8 are randomly arranged to form a three-digit number. (Digits are not repeated.) Find the probability that the number is even and greater than 800.
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.
A group of five students went to a hotel with 10 upper floors and a ground floor. The students simultaneously enter the elevator at the ground floor. The students choose their exit floors independently of each other. Determine the probability that they are all going to different floors when each student randomly chooses one of the 10 floors as their exit floor.
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.