What is the least number of people that need to be in a room such that there is greater than a 50 % chance that at least two of the people have the same birthday ?
Click here to see the solution.
Courtesy: Vibhaj Rajan
p.s. - For Remarks please hit the given link once. For Hint, hit it twice and for the solution, hit it thrice.
Hints: Probability, think how will it be not possible? Hit again for solution. |
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Solution:
At least 23 people should be there.
To find N such that probability of two people sharing the same birthday be more than 50%, we find N such that probability of no two people sharing same birthday be less than 50%.
Thus probability would be 364/365 * 363/365 * 362/365.... (N-1 terms)... (365 - (N-1) )/365 < 0.5
So, N = 23
For more information : http://en.wikipedia.org/wiki/Birthday_problem
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