kennaval wrote:
Twenty people at a meeting were born during the month of September, which has 30 days. The probability that at least two of the people in the room share the same birthday is closest to which of the following?
(A) 10%
(B) 33%
(C) 67%
(D) 90%
(E) 99%
The probability that at least two people sharing the same birthday = 1 - the probability that none of them sharing the same birthday
A = The number of ways of none of them sharing the same birthday = 30P20 = 30!/(30-20)! = 30!/10! = 11*12*...*29*30
B = The total number of possible ways of 20 people born in September = 20*20*....*20*20 = 20^30 ( each day has 20 options)
A/B = the probability that none of them sharing the same birthday
since B is much greater than A, A/B may equal 1%
--> The probability that at least two people sharing the same birthday = 1 - 1% = 99%
Answer E
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33% (02:14) correct 
