00:01
The probability of a bank making a mistake in processing a deposit is 0 .003.
00:10
And if 10 ,000 deposits are audited, that 10 ,000 would be our sample size.
00:18
What is the probability that there will be more than six mistakes made? so this is a binomial probability question, and it's binomial probability because there are only two outcomes, and we define those outcomes as success or failure.
00:51
Either they made a mistake or they didn't make a mistake.
00:54
The trials will be independent, and there are a fixed number of trials.
01:07
And in order to determine binomial probability, the probability of x successes is found by using the formula, the combination of n items taken x at a time, times p to the x power, times 1 minus p to the n minus x power.
01:38
So if you think about this particular problem, our n is already defined at 10 ,000, and our p is defined at 0 .003.
01:54
So now we've got to talk about x.
01:56
So in this case, we could have x being 0.
02:05
We might have no mistakes, or one.
02:08
We might have one mistake, or two, or three, or four, or five, or six, or seven, or eight, all the way up to the possible 10 ,000 mistakes.
02:24
Now, that's highly unlikely, but it's got a small possibility.
02:30
So what we want to do is we want to talk about each of their probabilities.
02:35
And our values that we're really concerned with is, what's the probability of more than six? so we're really interested in these probabilities right here.
02:50
But that list is super long, that would take a lot of calculations.
02:56
So instead, what we're going to do is we're going to use the characteristics of a probability distribution, or i should say a discrete probability distribution, and we know that the sum of all probabilities of all outcomes have to add up to one.
03:12
So what we'll do is we'll use this formula for the first seven.
03:17
So the first one, we'll find the probability that x equals zero, which would be 10 ,000 c0 times 0 .0, 0 .03 to the 0 .03 to the zero, times 1 minus 0 .000 -0 -03 to the 10 ,000 minus 0 power.
03:43
And in doing so, you will get a probability of 0 .049 -6 -4 -6 -4 -7...