00:01
We're looking at a binomial distribution.
00:03
We have six fail -safe components on a missile guidance system.
00:07
So, n is six.
00:09
Probability of each failing is 0 .1.
00:12
Okay, so we have these six independent trials, and each one has a 10 % chance of failure.
00:19
And we want to find some probabilities.
00:21
For the first one, what's the probability that two of them fail? so when we want an exact number of, in this case, components failing, we use the binomial formula, which is the probability, exactly x successes, is n choose x, p to the x, 1 minus p to the n minus x.
00:46
So we have these three terms to multiply.
00:50
The first term is for how many ways there are of putting your trials in order.
00:54
So we have four components working and two of them fail.
01:01
So that's one way you could have these components.
01:04
If you have them all in a line, these two could fail and these could be working.
01:08
You could also have that or that.
01:10
There's many ways of putting them in order.
01:11
How many? well, most calculators have a button.
01:15
This is a combination problem.
01:18
But if not, it's n factorial over x factorial and minus x factorial.
01:25
So it's six choose two.
01:28
Six choose two is 15.
01:31
There are 15 ways of putting them in order.
01:33
This is the the ones that fail, 0 .1 to the power of 2.
01:38
But the 2 that fail, this is the ones that are working, 0 .9 to power of 4.
01:43
When you multiply these, we get the solution.
01:47
So i'll do that.
01:49
Times 0 .9 to power of 4 gives me 0 .094 to 4 to 4 decimal places, 3 decimal places, 0 .098.
02:07
That's the first part.
02:09
Part b, more than two, fail.
02:12
So more than two means either three or four or five or six fail.
02:21
You could work out each of these with the binomial formula, then add them up.
02:25
I'm going to go the other way...