Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 5.4, Problem 1E
Program Plan Intro
To find the number of people in a room before the probability that someone has same birthday is at least
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13
possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), 4 possible suits (spades, clubs, hearts, diamonds),
and 13 cards in each suit (one of each rank).
A hand of 9 cards is drawn from a standard deck of 52 cards (assume all outcomes are equally
likely).
For each of the following questions, you should write your answer as an expression. Do not give the
final numeric value. For example, you should write C(4, 2)/24) instead of 0.375.
What is the probability that you are infected if a 95% accurate test returns a positive result? You are a member of a population where 2% of the people are infected.
A math class has 25 students. Assuming that all of the
students were born in the first half of the year – between
January 1st and June 30th– what is the probability that at
least two students have the same birthday? Assume that
nobody was born on leap day, so there are 181 possible
birthdays.
Chapter 5 Solutions
Introduction to Algorithms
Knowledge Booster
Similar questions
- The probability of event A is 55%. The probability of event B is 40%. The probability that A happens given that B has happened is 25%. What is the probability that both A and B happen? 95% 70% 65% 10% 15%arrow_forwardThere are 7 balls hidden in a box (3 blue and 4 green). If you first select a green ball and do not replace in the box, what is the probability that the second ball you select from the box will also be green? [Your answer can be written either as a fraction or decimal]arrow_forwardA and B stand in a line at random with 10 other people. What is the probability that there are exactly 3 people between A and B?arrow_forward
- The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses fewer than 400 minutes? 0 0.023 0.159 0.977arrow_forwardMedical records show a sample population of 1000 people, of those 1000 people, 98% do not have a terminal illness and 2% do have a terminal illness. A Health Insurance company would like try out a new cheaper test for terminal illness. Their results show that 98% of the people that do have a terminal illness test positive, while 1% of the people who do not have a terminal illness test positive for one. A corporation known as Ken’s Kids is concerned about patients that are slipping through the cracks with this new medical testing. If the new medical testing is adopted, what % of the people will be misdiagnosed as not having a terminal illness, but really have one? Assuming a population of 200 million people, how many people that have a terminal illness, given this new testing will never know that they do? (Please show all work , and have a legend for symbols).arrow_forward138 If each book in a library has has an ISBN number that begin with 2 distinct letters followed by 5 distinct non zero digits. What will be the chance of selecting a book whose ISBN number has first letter a consonant and last digit an odd number 12:39 PMarrow_forward
- A group of individuals are living on an island when a visitor arrives with an unusual order: all blue-eyed people must leave the island immediately. Every evening at 8:00 p.m., a flight will depart. Everyone can see everyone else's eye colour, but no one knows their own (nor is anyone allowed to tell them). Furthermore, they have no idea how many people have blue eyes, but they do know that at least one person has. How long will it take for the blue-eyed individuals to leave?arrow_forwardQ3/ For a given exam, there is 40% of the students passed math test, and 30% passed biology test, and 20% passed both math and biology tests. What is the probability that a randomly selected student failed biology given that he passed math? (Use Venn diagram)arrow_forwardRecall the airplane puzzle from the lab: the first person to get on the plane picks a random seat, the rest sit in their assigned seat if it is available, otherwise pick a random available seat. Assume person i is assigned the seat i. Suppose person 18 came in and discovered that their seat is taken. Assuming that the last person's seat, which is seat number n=32 on this plane, it is still available, what is the probability that person 18 will randomly pick it? Hint: to make sure your formula is correct, check that it works for the passenger right before the last one. Enter your answer as a decimal number with at most three digits after the decimal point, rounding if necessary. For example, if your answer is 1/3, round it and enter it as 0.333, if your answer is 2/3, enter it as 0.667, and if your answer is 1/2, enter it as 0.5. Your Answer:arrow_forward
- P = total number of individuals infected on any day N = total number of individuals infected on day zero R = number of individuals infected by contact with 1 person Find the number of day where P = 750 Pzero (ppl with the disease on day zero) = N P1 ( ppl with the disease of day 1) = N + NR = N(1+R) P2 = N +NR + R(N + NR) = N + NR + NR + NR^2 = N + 2NR + NR^2 = N(1 +2R + R^2) = N(1 + R)^2 P3 = (N + 2NR + NR^2) + R(N +2NR +NR^2) = N + 2NR + NR^2 + NR +2NR^2 + NR^3 = N + 3NR + 3NR^2 + NR^3 = N(1 + 3R + 3R^2 + R^3) = N(1 + R)^3 Pi (people with the disease on day i) = N(1+R)^i use pythonarrow_forwardExample 7: An internet company provides TV and Internet services in a certain city, 60% of all houses get Internet service from that company, 80% get TV service from that company, and 50% get both services from that company. If a house is randomly selected, 1) what is the probability that it gets at least one of these two services from the company? 2) what is the probability of the event that it get only TV service? 3) what is the probability of the event that a house get only Internet service ? 4) what is the probability of the event that it get exactly one service ? 5) what is the probability that a house get none of each service?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole