|
Search: id:A091673
|
|
|
| A091673 |
|
Numerator Q of probability P=Q(n)/365^(n-1) that exactly two out of n people share the same birthday. |
|
+0
3
|
|
| 1, 1092, 793884, 480299820, 261163522620, 132358677731280, 63798093049771080, 29612552769907347240, 13345042642324219106280, 5872442544965392834838400, 2533775368098060137659608000, 1075256447734638237381213700800
(list; graph; listen)
|
|
|
OFFSET
|
2,2
|
|
|
COMMENT
|
A 365 day year and a uniform distribution of birthdays throughout the year is assumed.
|
|
LINKS
|
P. Le Conte, Coincident Birthdays.
Eric Weisstein's World of Mathematics, Birthday Problem. Section in World of Mathematics.
|
|
FORMULA
|
P(n)=n!*sum_{i=1..floor(n/2)}(binomial(365, i)*binomial(365-i, n-2*i)/2^i)
|
|
EXAMPLE
|
a(3)=1092 because the probability in a group of 3 people that exactly two of them share the same birthday is (1/365^3)*3!*binomial(365,1)*binomial(364,1)/2=
(1/365^2)*3*364=(1/365^2)*1092.
|
|
MATHEMATICA
|
P[n_] := (n! Sum[ Binomial[365, i]*Binomial[365 - i, n - 2i] /2^i, {i, 1, Floor[n/2]}]/365); Table[ P[n], {n, 2, 13}] (from Robert G. Wilson v Feb 09 2004)
|
|
CROSSREFS
|
Cf. A014088, A091674 gives probabilities for two or more coincidences, A091715 gives probabilities for three or more coincidences.
Sequence in context: A043856 A043864 A043873 this_sequence A096082 A138698 A023698
Adjacent sequences: A091670 A091671 A091672 this_sequence A091674 A091675 A091676
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 03 2004
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v, 9rgwv(AT)rgwv.com), Feb 09 2004
Broken links corrected by S. R. Finch (Steven.Finch(AT)inria.fr), Jan 27 2009
|
|
|
Search completed in 0.002 seconds
|
