00:01
For this problem, i'll note that it's going to be easier to first start off by just trying to find the probability of all of the birthdays being unique.
00:12
If we can find the probability of every birthday being unique, then we can find the probability of at least two people sharing a birthday just by taking one minus the probability of all the birthdays being unique.
00:25
So to find the probability of all the birthdays being unique, we can first of all think about okay, if we just have one person, then it's impossible to have any pairs.
00:36
So there is a 100 % chance or a probability of one that with one person, there are no pairs.
00:43
If we have two people, then we have that for the second person, there are 364 different days that they could have been born on out of 365.
00:57
So the probability that these that when we have two people, there are no pairs be 364 out of 365.
01:05
And then if we think about okay, now we have three people for that third person, the probability representing okay, is the third person does the third person have a unique birthday? well, there are 363 different days on which they could have been born out of 365, and so on.
01:24
So we can see that the probability of all of the birthdays being unique would be p1 times p2 times dot dot dot, all the way up until times p23, since we have 23 people...