Find the probability that of 25 randomly selected people no 2 share the same birthday? also.>>?

Question

the probability that at least 2 people sahre the same birthday?

with details and resons please

Answer 1

This is a fun problem

The probability that two people do not share the same birthday is

365/365 *  364/365

For three people,  it's

365/365 * 364/365 * 363/365

etc.

The break point comes,  I believe  at 26 people where the probability that 2 people will not share the same birthday goes below 50%.  At 30 people,  it's really pretty low.

Answer 2

(Note I completely re-wrote this to simplify)

The odds of the 1st person in the group not sharing is 100%, or 365/365 (he can have any birthdate, it doesn't matter!)

The odds of the 2nd person not sharing is 364/365 (she can't have the same birthday as the first guy, but the other 364 days are fine)

For the 3rd person, it's 363/365.

And so on...

The overall probability that nobody in a group of 25 shares a birthday is:

365/365 * 364/365 * 363/365 * ... * 341/365

The answer here is 0.4315, or about 43.2% chance.

Since the odds of NOBODY sharing is .4315, then the probability of SOMEBODY (at least 2 people) sharing must be the converse probability:

1 - .4315 = .5685, or about 56.9% chance.

Hope that helps.

EDIT - I reject Blah's nit and demand a retraction!  :-)  I think I say above that .4315 is approximately 43.2%. The number 42 does not appear in this answer, even though it is...you know...the Ultimate Answer. :-)

Answer 3

Frank's method and answer are incorrect.

The other method (365/365*364/365*...341/365) is correct.

Boid's answer is correct except for a small nit -- .4315 rounds to 43, not 42. (I got 43.13)

Answer 4

1)Probability that no other person will have the same birthday:

(364/365)^24 = 0.92352

So, the probability that at least one person will have same birthday is:

1 - 0.92352 = 0.076478

2) same reasonning for two persons share the same birthday:

    365/365 x 364/364 x 363/365 x ... = 0.29368

so,  P(least 2 people share the same birthday) = 1 - 0.293684

                                                                    = 0.70691 (answer)