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Image_of_God
Guest
Mathematical equations for probability are essentially idealistic and theoretical. That is to say, they would work if everything happened according to mathematical laws, but of course they don’t. Probability might be good for gathering statistical information about the future, but it just isn’t reality. There is no certainty.Ok, math course is coming up. Since the people are randomly selected, the probability that any specific person was born on any specific day of the year is 1 in 366. We suppose an equal distribution, which is not exactly correct, because more people are born in the summer, than in winter. But this discrepancy is not relevant, it actually raises the chance of a “duplicate birthday” a little bit.
We talked about 30, randomly selected people. We can generalize and talk about “n”, randomly selected people, and then look at the special case, where n = 30.
Now with any selected group, there are two possibilities: 1) all people were born on different days, and 2) at least two people were born on the same day. Let “p” be the probability of case 1). Obviously “1 - p” will be the probability of case 2).
It is much simpler to calculate the value of “p”, and then subtract the value from 1. We shall call it a “good” day if it is separate from all the previously “selected” days.
Now, for the “meat”. The first person selected could have been born on any day, so his chance of being born a good day is 366/366 (no days have been taken yet). The second person only has now 365 “good” days to choose from (one is already taken), so his chance of selecting a good day is 365/366. For the third person there are only 364 days remaining. For the fourth one, only 363 days remain, and so on. Since the birthdays are independent from each other, the chance that “n” people all were born on a different day of the year is:
p = (366/366)(365/366)(364/366)(363/366)…*((366 - (n-1))/366)
You could use a hand-held calculator to find out the value of “p” for any given “n”. Then subtract this value from 1 to get the probability of having at least one duplicate birthday. For the value of 30 the probability of having at least one duplicate birthday is about 73% - amazingly high. For 40 random people the probabilty is over 90%. For 60 people it is over 99%. It is almost impossible to collect 60 random people and not find at least two of them who were born on the same day of the year.
There is nothing intuitive or self-evident about this.
Which brings me back to the idea that you chose the number you did because of your intuition and reason.
Lots of things are accepted as self-evident - and rightfully so. That is not the problem. The problem is to assume that everything which **looks like **self-evident is supposed to be accepted as self-evident. This is the point when the adage should be: “shut up and calculate” or “shut up and measure” - depending on the topic.
I am by no means saying that everything that *looks *self-evident should be accepted as such. I only state that we use our reason to decide what is true among others. It’s what you have done numerous times on this thread while refusing to admit it.