00:01
Okay, so we just got a question about the binomial distribution here.
00:04
Now, remember with binomial, we've got n trials of something that has a probability p of being a success, and the only other outcome is failure with probability 1 minus p.
00:18
And then the probability, so if x follows, we say x follows a binomial distribution with parameters n for the number of trials and p for the probabilities of success.
00:27
And the probability that x has k successes is then just given by n choose k times p to the k times 1 minus p to the n minus k for k successes and p and n minus k failures.
00:44
So that's what we're going to use in the rest of the question.
00:47
Okay, then question one says we've got five trials with a probability 0 .7 of success and they want us to construct a binomial distribution with answers reported to three decimal places.
01:02
So we've got five trials, so you can either have zero, one, two, three, four or five successes.
01:14
And the probability, for instance, that x equals three, let's do, is going to be five, choose three.
01:20
Using the formula we wrote above, it's going to be five, choose three times zero point seven cubed, times 0 .3 to the 5 minus 3, which is 2, so 0 .3 squared.
01:32
And that turns out to be to three decimal places, 0 .309.
01:40
And if you do the same for all of them, you get 0 .132 here, 0 .002 here.
01:53
Oh, sorry, i've skewed these...