00:02
So we have a sample size here 9 right we're giving some probability to be 0 .51 so we're going to call p the probability of success that's going to be 0 .51 so from the given information we're going to be using a binomial distribution with n np so for a binomial distribution the probability of x it was x for example is given by n completion x times p to the x times q to the n minus x let's be in mind that q is 1 minus p so in this case it's going to be 1 minus 0 .51 and 0 .49 so we're asked to find the probability that x is rather than equal to 5 that is at least 5 so you can rewrite this as the as one minus the probability of x less than five, which is one minus the probability of x equals 0, plus the probability of x equals 1, plus the probability of x equals 2, and then for 3, and then 4.
01:42
So let's do for 0 up to 4 and then we're going to add them up and then subtract from 1.
01:55
So for p x equals 0, that's going to be 9 combination 0 times 0 .51.
02:07
So we're using a formula, right? using that formula right there.
02:13
So times 0 .49 exponent 9 minus 0, which is just 9.
02:21
So this one is going to be 0 .00163.
02:29
Then we go ahead to x equals 1.
02:34
There's going to be 9 combination 1 times 0 .51 x .1 times 0 .49 exponent 9 minus 1.
02:45
If you crank this out, you get 0 .0 5125.
02:55
For x equals 2, you have 9 ,000 ,000.
02:59
2 times 0 .51 squared times 0 .49 s p .9 minus 2.
03:09
This is going to be 0 .06 3 .1.
03:17
We got 2 more.
03:19
9 x equals 3.
03:22
That's 9 combination 3 times 0 .51 2 times 0 .49 .9 minus 3.
03:35
That should be 0 .154229.
03:44
And the last one, x equals 4...