# Puzzling Probability

• January 13th 2006, 11:36 AM
ThePerfectHacker
Puzzling Probability
A friend and I had debate what the probability of being born on Feb 29 is?
1)I said it is Probability of Leap year and Feb 29 which is $\frac{1}{4}\frac{1}{366}=\frac{1}{1464}$
2)He said in 4 full years there are 1461 days thus the probability is $\frac{1}{1461}$

Who is correct? Both explainations are reasonable.

I am thinking that the probability of a year being leap is not exactly $1/4$ but close to it. Which is why he and I have a minor discrepancy.
• January 13th 2006, 11:53 AM
CaptainBlack
Quote:

Originally Posted by ThePerfectHacker
A friend and I had debate what the probability of being born on Feb 29 is?
1)I said it is Probability of Leap year and Feb 29 which is $\frac{1}{4}\frac{1}{366}=\frac{1}{1464}$
2)He said in 4 full years there are 1461 days thus the probability is $\frac{1}{1461}$

Who is correct? Both explainations are reasonable.

I would go with your friends answer. Being born in a leap year and on
Feb 29th are not independant events, and so the product rule does
not apply.

Quote:

I am thinking that the probability of a year being leap is not exactly $1/4$ but close to it. Which is why he and I have a minor discrepancy.
RonL
• January 13th 2006, 12:05 PM
dud
According to textbook, this is something like;

P(Leap Year):
Desired Events / Possible Events = P(L)
$
P(L) = \frac{1}{4}
$

P(29th of February):
Desired Events / Possible Events = P(D)
$
P(D) = \frac{1}{366}
$

$
P(L) \bigcap P(D) = P(L) \times P(D) = \frac{1}{4} \times \frac{1}{366} = \frac{1}{1464}
$

Albeit your friend gets the same answer, he sort of assumes a span of 4 years by multiplicating 366 with 4 doesn't he?
As opposed to calculating 1: probability of being a leap year. 2: probability of being actually born on 29th of February.
• January 29th 2006, 06:06 PM
rabeldin
Probability of being born on Feb 29
It sounds as if you have made some assumptions about classes of events that have equal probabilities. Do you assume that every day in the year has equal probability of being the day someone is born? What if you knew the date of conception? What if you knew the mother is pregnant?

Such complicating factors are meant to provoke you to examine your assumptions.