Question

Birthdays- of the 44 US presidents, only Polk (11th) and Harding (29th) share a common birthday (November 2). What is the probability that there has been no common birthday since Calvin Collidge (30th)?

I know the answer is .25, but I am not sure how to solve it.

Answer 1

Previous problems were set up like: 44 presidents, share common b-day. Find the probability that at least 1 common b-day among 29 presidents.

\[P (at least one common birthday day of 29) --> 1 - (\frac{ 365 npr 29 }{ 365^{29}})\]

Answer 2

which is .6809

Answer 3

There have been 15 presidents since Calvin Coolidge (including C.C.). For two presidents, the probability that the second president doesn't have the same birthday as the first is 364/365. Then the probability that those two presidents' birthdays are different and a third president's birthday is different from either of theirs is 364/365 * 363/365. When we continue this reasoning we find that the probability that none of the 15 presidents share the same birthday is given by:
\[P(0\ shared\ birthdays)=\frac{364}{365}\times\frac{363}{365}\times\frac{362}{365}\times\frac{361}{365}........ \times\frac{351}{365}=0.75\]
Consequently the probability that some of the 15 presidents share the same birthday is 1 - 0.75 = 0.25.

Answer 4

@kropot72 is there a way you can do that on a calculator?

Answer 5

@kropot72 I solved it \[\frac{ 365 npr 15 }{ 365^{15} } = .75\] thanks for your help

Answer 6

\[364\times363\times362\times361\times\ ..................\times351=5.565165\times10^{35}\]
\[365^{14}=7.44904\times10^{35}\]
\[\frac{5.565165}{7.44904}=0.747\approx0.75\]