Question

(The Birthday Problem) It is known that there are as many as n people in a...

(The Birthday Problem) It is known that there are as many as n people in a room
a. How big is the chance that no one has the same birthday?
b. What is the value of n so that the probability of problem (a) is less than 50%?

0 0
Add a comment Improve this question Transcribed image text
Answer #1

a)P( no one has the same birthday )=P(all n people have different birthdays)=P(selecting n days from 365)

=(365*364*363*.....(365-n+1)/365n

b) P( no one has the same birthday )=(365*364*363*.....(365-n+1)/365n <0.50

solving above by putting values , n=23

Add a comment
Know the answer?
Add Answer to:
(The Birthday Problem) It is known that there are as many as n people in a...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • Birthday problem). Assume that a host invites n guests and that days of all n+1 people...

    Birthday problem). Assume that a host invites n guests and that days of all n+1 people are independent and uniformly distributed acros Exercise 1.10 ( the birth all the 365 days of the year 1. Prove the following: The probability that two of the guests share the same birth- day is larger than one-half if and only if n 2 23. 2. How large should n be so that the probability that at least one of the guests has the...

  • The birthday problem is as follows: given a group of n people in a room, what...

    The birthday problem is as follows: given a group of n people in a room, what is the probability that two or more of them have the same birthday? It is possible to determine the answer to this question via simulation. Using the starting template provided to you, complete the function called calc birthday probability that takes as input n and returns the probability that two or more of the n people will have the same birthday. To do this,...

  • in python The birthday paradox says that the probability that two people in a room will...

    in python The birthday paradox says that the probability that two people in a room will have the same birthday is more than half, provided n, the number of people in the room, is more than 23. This property is not really a paradox, but many people find it surprising. Design a Python program that can test this paradox by a series of experiments on randomly generated birthdays, which test this paradox for n = 5, 6, 7, ..., 50....

  • Random variables and expected value Shared Birthday Height Arrangements Example: How many pairs of people in...

    Random variables and expected value Shared Birthday Height Arrangements Example: How many pairs of people in this room do we expect to share a birthday? Example: If we randomly arrange n people in a line, what is the expected number of people who are taller than all adjacent people? Assume each person's height is different (no ties). If there are 30 people in the room, how many pairs of people are there? What is the probability that two particular people...

  • The R command sample (1:365,23, replace=T) > simulates birthdays from a group of 23 people. The...

    The R command sample (1:365,23, replace=T) > simulates birthdays from a group of 23 people. The expression 2 %int table (sample (1:365, 23, replace=T)) can be used to simulate the birthday problem. It creates a frequency table showing how many people have each birthday, and then determines if two is in that table; that is, whether two or more people have the same birthday. Use and suitably modify the expression for the following problems (a) Simulate the probability that two...

  • please help me understand this problem. k people in a room. We would like to find...

    please help me understand this problem. k people in a room. We would like to find the probability that any two people 5. Suppose that there are have birthdays within a day of each other (which we'll call "near-day birthdays"). The number of pairs and the probability that any two people are born within a day of each other is of people would be S4Therefore, we would expect the average number of near-day birthday pairs to be be a Poisson...

  • Explain the birthday paradox. Why 253 people would need to be in the room for 50...

    Explain the birthday paradox. Why 253 people would need to be in the room for 50 percent chance to get the same birthday?

  • Problem 1. Suppose that we take a random sequence of numbers modulo n. The proba- bility...

    Problem 1. Suppose that we take a random sequence of numbers modulo n. The proba- bility that the first k terms are all distinct is n - 1 п 2 n - (k – 1) P(n, k) = 2 п п п as we saw in class. For this problem, you will want to write a (very short) program to compute this number, but you do not need to submit it this time. (For both parts, you can submit a...

  • What is the probability that in a room of n people, at least three of them...

    What is the probability that in a room of n people, at least three of them have the same birthday? Explain all the terms in your solution. What is the fewest amount of people such that the probability of at least three of these people having the same birthday is greater than 1/3? You will have to code your solution from the first question and plug in values for n. Include the code snipped you used to solve this.

  • (1 point) Consider the experiment, called the birthday problem, where our task is to determine the...

    (1 point) Consider the experiment, called the birthday problem, where our task is to determine the probability that in a group of people of a certain size there are at least two people who have the same birthday (the same month and day of month). Suppose there is a room with 10 people in it, find the probability that at least two people have the same birthday, Ignore leap years; assume each year has 365 days. Answer

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT