Birthday Problem: Find the Probability of 3 People Sharing the Same Birthday

  • Context: Undergrad 
  • Thread starter Thread starter skip_it2
  • Start date Start date
Click For Summary
SUMMARY

The probability of three randomly selected individuals sharing the same birthday is calculated as (365/365)(1/365)(1/365), resulting in a probability of 0.00000751. Conversely, the probability that none of the three individuals share a birthday is calculated as (365/365)(364/365)(363/365), yielding a probability of 0.992. A direct counting approach is recommended for a clearer understanding, involving the calculation of total birthday possibilities and the respective counts for both scenarios.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with combinatorial counting methods
  • Knowledge of the birthday problem in probability theory
  • Ability to perform calculations involving fractions and probabilities
NEXT STEPS
  • Research combinatorial probability techniques
  • Learn about the generalized birthday problem
  • Explore applications of probability in real-world scenarios
  • Study advanced probability distributions and their implications
USEFUL FOR

Students in mathematics, statisticians, educators teaching probability, and anyone interested in understanding the intricacies of the birthday problem in probability theory.

skip_it2
Messages
1
Reaction score
0
Three people are selected at random. Find the probability that

(a) all three share the same birthday:

(365/365)(1/365)(1/365) = 0.00000751

(b) none of the three shares the same birthday. Assume 365 days in a year.

(365/365)(364/365)(363/365) = 0.992
 
Last edited:
Physics news on Phys.org
Sorry - I was thinking this was a homework forum problem - is it homework?
Try a direct counting approach:
1) Figure out how many possibilities there are for birthdays for the three (no restrictions)
2) For 'a', count the number of ways all three could have the same birthday, then divide by the answer to '1'
3) For 'b', count the number of ways none have the same birthday, then divide by the answer to '1'

Thanks for adding your work. It wasn't here before.
 
Last edited:
Your answers are correct.
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
5K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
1
Views
1K
Replies
8
Views
4K
  • · Replies 15 ·
Replies
15
Views
28K
  • · Replies 2 ·
Replies
2
Views
7K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K