Class Has 25 Students. Let A Be The Event That 2 Or More Of These Students Share The Same Birthday (day & Mont
Feb.24, 2010 in
mont tremblant
(day & month) All 365 days are equally likely. Determine P(A) and give the general form of the equation for any number of students. (HINT: It may be easier to consider complementary events)
I need the equation and the solution.
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February 24th, 2010 at 5:59 pm
The probability that no one in a room of 25 people share a birthday is: 0.4313003
The probability that at least two people share a birthday in a room of 25 people is: 0.5686997
this is a well documented problem called the birthday paradox.http://en.wikipedia.org/wiki/Birthday_pr…
February 24th, 2010 at 6:35 pm
The hint is the key, it’s easier to compute the complimentary event, ie B that no two students have the same birthday.
P(A)=1-P(B)
Computing P(B)
For the first kid, we can pick any day (365 of 365)
For the second kid, we can pick any day except one (364 of 365)
For the third kid, there are 363 of 365.
etc.
so P(B)=(365/365)(364/365)…(341/365)
=(365*364*…*341)/(365^25) or 365!/(340!*365^25)
~=0.4313