Timeline for The Birthday Problem
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 15, 2013 at 21:22 | comment | added | vadim123 | My pleasure, happy hunting. I'd recommend posting it as a standalone question, you'll have more luck that way. | |
| Jul 15, 2013 at 21:20 | comment | added | Au101 | I agree with you on $n = 4$ and $n = 5$. I think I must have done, thank you so much vadim, that's perfect. So we say that given a group of 5 people, the probability that two of them will share birthdays with a month (specifically 30 days) of each other is 0.89. That's great. I'll now have a go at Question 3 | |
| Jul 15, 2013 at 21:15 | comment | added | vadim123 | I think you mistyped the formula. For $n=5$ I get $0.885$, while for $n=4$ I get $0.705$. | |
| Jul 15, 2013 at 21:12 | comment | added | Au101 | For question 2: If I set $n = 1$ $P = 1$ (well, not quite, but W|A gives the answer as so close to 1 it makes no difference. Well, this is odd, I don't really understand what this result means, but $n = 2$ gives an answer fantastically close to 1 again, so I can only assume that even with just 2 people, their birthdays are almost certainly within a month of each other. This is plainly false? | |
| Jul 15, 2013 at 21:11 | comment | added | Au101 | Question 1 I can completely understand. If I try $n = 9$ I get $P(9,7,365) = 0.81$ (3sf). So, from that, we can see that if we randomly select 9 people, the probability that two of them will share birthdays within 7 days of each other is 0.81. Which is really cool. | |
| Jul 15, 2013 at 21:01 | comment | added | vadim123 | But you want integer $n$; just try $n=8, 9$ to see what happens in q1. Same for q2, just try $n=1,2,3,4,\ldots$. | |
| Jul 15, 2013 at 20:53 | comment | added | Au101 | Okay, for question 1: Wolfram|Alpha spits out four values of $n$. One is negative and two are in the nineties, but $n \approx 8.35709466412574\dots$ is good. And if I try it with $n = 9$, I get $P = 0.81$ (3sf) which seems to work. For question 2: I get a very low value of $n$ with $k = 30$, specifically $n \approx 0.00783908832757675\dots$ which I'm not really sure how to interpret. (I should clarify I merely set the equation above equal to 0.75 and filled in the values of $m$ and $k$, thus giving the exact value of $n$ that would give a probability of 75%) | |
| Jul 15, 2013 at 20:27 | history | answered | vadim123 | CC BY-SA 3.0 |