00:01
All right.
00:03
So here we go.
00:04
We got a nice binomial probability exercise here.
00:08
And so we suppose 50 % of the applicants to an engineering school of women.
00:13
Admissions, committee reviews, applications, and groups of 100.
00:16
Find the probability that the number of women in the next group is all these probabilities.
00:22
And we're around to the fifth decimal place.
00:25
So we're going to do less.
00:26
Well, it's binomial because we're assuming the choice of one applicant has no impact.
00:34
On the admissions of another one.
00:39
Or the fact that one applicant is a woman has no impact on the next one, being a woman.
00:49
So there's that.
00:50
And you could either be a woman or not be a woman.
00:54
So it's discrete outcomes.
00:59
And there's, yeah, so we're going to assume binomial.
01:02
And that tells us we can use p to the x times one minus p.
01:08
So the n minus x, and we also have n choose x is that, and this is the probability of some x.
01:20
So we want less than or equal to 23, so probability that x is less than or equal to 23.
01:30
So that's going to be equal to, i'm going to use the sum.
01:33
We're just summing up a bunch of probabilities here.
01:35
X is zero up to 23 of out of 100.
01:43
Choose x and the probability is 0 .5 x and then we have 0 .5 to the 100 minus x we're summing all those together and then we end up with something uh it's it's ridiculously small it's like it's uh i get 2 .7568 times 10 to the i mean it's it's crazy small that you have that few applicants when there's a 50 % chance of being an applicant that'd be pretty pretty rare that's we'd say that's a that's very unlikely so between 21 and 36 this what we're going to do is we use the same kind of sum formula here probability that x is between 21 and it's inclusive so that's important because we're going to sum the x starting at 21 up to 36.
02:56
We have 100.
02:57
And we do the same thing, x.
02:59
And we have the same formula here, 0 .5 to the x times 0 .5 to the 100 minus x.
03:05
We use our calculating devices and we get 0 .00332.
03:16
There we go...