# Probability

dollymay | 17:29 Mon 22nd Mar 2021 | Science
Not sure if I am in the right section here. But back when I studied probability at college, I remember a standard question was what was the probability of the number of people having the same birthday in, say, an audience of 100. But cant remember at all how to calculate, but remember being surprised at the answer. Lightweight question for Science I'm afraid.

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In an audience of 100 people there is a 99.9999692751% chance of any two of them sharing a birthday (just the date, not the year). In fact the probability becomes greater than 99% once the audience reaches 57 in number. Beyond that the probability raises fractionally but insignificantly until it reaches 100% at 365 (my calculations do not account for Feb....
17:56 Mon 22nd Mar 2021
Unsurprisingly, the wiki link covers most of it -- the key point is to realise that it's easier to calculate the probability that nobody shares a birthday, which becomes the product (365/365)*(364/365), etc. You keep subtracting one from the top part, as fewer and fewer "untaken" days remain. It's still a bit of a surprise that you only need 23 students to get the overall product to about 0.5, but that's just how numbers work.
In an audience of 100 people there is a 99.9999692751% chance of any two of them sharing a birthday (just the date, not the year). In fact the probability becomes greater than 99% once the audience reaches 57 in number. Beyond that the probability raises fractionally but insignificantly until it reaches 100% at 365 (my calculations do not account for Feb. 29th).

The usual question along these lines is how many people must be present before there is a greater than even chance that any two will share a birthday – to which the answer is 23 (50.7297%.
Do you think there is a high or low chance that the next person you see will have more than the average number of legs?
A very high chance. In fact, I don't think I've ever seen anybody with the (mean) average number of legs. :-)
Well done, NJ
I went to an ice hockey game a couple of years ago and a guy sat next to me who I had never met before. We got chatting and eventually found out that we shared the same Birthday. There were over 9,000 people at that game! I wonder what the probability of having the same Birthday and sitting next to each other is?
I gave birth to my daughter on my birthday!! What are the odds on that?
A little longer than 364/1.
Depends if the conception was a random event, though, Jim :-)
I met a girl at youth club who came from the next borough and it turned out we were not only born on the same day but in the same hospital - we joked that we could have been swapped at birth.
What is the probability that the lottery ticket you bought will win the lottery ?

50%

You'll either win it or you won't.
:-0 NJ!!

Question Author
Thank you all, the last paragraph from New Judge was the question I remembered, I'm still surprised at the answer and still don't really understand, tbh, but that's me. Thanks again.
I'm sure not, chrissa!

The reason I mentioned the "random" thing is that the odds are only true for random events. Like a roulette wheel with 37 slots; it is 36/1 that any individual number will be the winner. With something like conception, if you confine your "activities" to, say, predominantly the winter months (say four times as much in the winter than in the summer) then the odds against you conceiving (and so your chid being born on a particular date) are not even across the year and the 364/1 figure would not hold good.
And probability is often misunderstood by the human need to put order out of perceived chaos. E.g. in a four-player card game where all cards are dealt out at the start, the odds of each player getting all 13 cards of the same suit is precisely the same as the four players getting any other combination of the cards. Similarly, the odds against Saturday's six lottery numbers coming up next Saturday is exactly the same as any other six numbers coming up.
I don't understand the legs one.
Yes Jim. A few months back there was a lottery somewhere (in Africa, I think) where numbers 1,2,3,4,5 and 6 were drawn. Everybody believed it was fixed. But as you say, that combination is the same as any other. It's just that the consecutive numbers are noticed as "special" whereas in fact all combinations are all equally special.
I'll need to check my lottery tickets for last Saturday, don't often do it.
//I don't understand the legs one.//

Some people have only one or even no legs jd. (I don't know of anybody with more than two). So the average number of legs possessed across the entire population is 1.9999999 (or whatever).

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