Absolute Java (6th Edition)
6th Edition
ISBN: 9780134041674
Author: Walter Savitch, Kenrick Mock
Publisher: PEARSON
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Chapter 16, Problem 3PP
The birthday paradox is that there is a surprisingly high probability that two or more people in the same room happen to share the same birthday. By birthday, we mean the same day of the year (ignoring leap years), but not the exact birthday that includes the birth year or time of day. Write a
The program should use simulation to approximate the answer. Over many trials (say, 5,000), randomly assign birthdays (i.e., a number from 1-365) to everyone in the room. Use a HashSet to store the birthdays. As the birthdays are randomly generated, use the contains method of a HashSet to see if someone with the same birthday is already in the room. If so, increment a counter that tracks how many times at least two people have the same birthday and then move on to the next trial. After the trials are over, divide the counter by the number of trials to get an estimated probability that two or more people share the same birthday for a given room size.
Your output should look something like the following. It will not be exactly the same due to the random numbers;
For 2 people, the probability of two birthdays is about 0.002
For 3 people, the probability of two birthdays is about 0.0082.
For 4 people, the probability of two birthdays is about 0.0163
…
For 49 people, the probability of two birthdays is about 0.9654
For 50 people, the probability of two birthdays is about 0.969
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What is the probability that in a classroom of x people, at least 2 will be born on the same day of the year (ignore leap year)? Use a Monte Carlo Simulation and a frequency table to write a program that calculates this probability, where the number of people (x) in the simulated class is given by the user. The probability for a class of size 23, should be right around 50%.
NO language of "break" or "true" please!
Please use the outline given below for the code:
What is the probability that in a classroom of x people, at least 2 will be born on the same day of the year (ignore leap year)? Use a Monte Carlo Simulation and a frequency table to write a program that calculates this probability, where the number of people (x) in the simulated class is given by the user. The probability for a class of size 23, should be right around 50%.
I have an outline for the code but please only use python language and NO "break", "true" language
import mathimport random
# create and initialize frequency table:ft = []k = 0while(k < 365) : ft.append(0) k = k+1
# Allow the user to determine class size:print("Please type in how many people are in the class: ")x= int(input())
success = 0
# Simulate:c = 0while(c < 10000) : # Step 1: re-initialize the birthday frequency table (it must be re-initialized for each play-through (why?): k = 0 while(k < 365) : ft[k] = 0 k = k+1 # Step 2: randomly get x birthdays and update frequency table: k =…
What is the probability that in a classroom of x people, at least 2 will be born on the same day of the year (ignore leap year)? Use a Monte Carlo Simulation and a frequency table to write a program that calculates this probability, where the number of people (x) in the simulated class is given by the user. The probability for a class of size 23, should be right around 50%.
PLEASE use the code outline given below to answer this question:
import mathimport random
# create and initialize frequency table:ft = []k = 0while(k < 365) : ft.append(0) k = k+1
# Allow the user to determine class size:print("Please type in how many people are in the class: ")x= int(input())
success = 0
# Simulate:c = 0while(c < 10000) : # Step 1: re-initialize birthday frequency table (it must be re-initialized for each play-through (why?): k = 0 while(k < 365) : ft[k] = 0 k = k+1 # Step 2: randomly get x birthdays and update frequency table: k = 0 while(k < x): # your code…
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Absolute Java (6th Edition)
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