Probability?

Question

100 people 365days, whats P(atleast two have birthday on the same day)

well can anyone get me 100% correct answers. There are all different answers and i am confused

Answer 1

this is Chemistry section man!!

Answer 2

1 - 365*364*363......*266/365^100

=1 - 365 P 100 / 365^100

P(atleast two have birthday on the same day)
= 1 - P(no two have birthday on the same day)

total no of ways in which 100 people may have birthday = 365^100

the first one may have birthday in 365 ways.
for, no two having the same bithday,the 2nd one may have birthday in 364 ways for each of these 365 ways of the first one.
ie. the first two may have different birthdays in 365*364 ways.

procceding similarly, the 100 people may have different birthdays in 365*364*....*266 ways.

so, P(no two have birthday on the same day)
= 365*364*....*266/365^100
= 1 - 365 P 100 / 365^100

using the complement rule,
P(atleast two have birthday on the same day)
= 1 - 365*364*....*266*265/365^100
= 1 - 365 P 100 / 365^100 [ here P = permutation]

u shouldn't have asked it in chemistry section, instead of math.

Answer 3

[365*364*363*.....266]/{365 raised to the power of 100}

Answer 4

1/365 * 364C98/364C1