00:01
Here we have a binomial distribution with parameters n equals 5 and p equals 0 .76.
00:07
So one way we can say that if our random variable is x, we can say it has a binomial distribution with parameters 5 and 0 .76.
00:16
And we are looking for the probability that this random variable x is equal to 4.
00:23
So we will be using the binomial distribution formula, the probability function, which, just to recall, is probability that x equals k is given by n choose k times p to the k power times q to the n minus k.
00:42
So this binomial coefficient n choose k can be written as n choose k or it can be written as n factorial over k factorial times n minus k factorial.
00:56
That's the formula we would use to evaluate it.
00:59
Most calculators have a function to evaluate these binomial coefficients, but if not, we could always use the factorials for it.
01:06
And then q is always equal to 1 minus p.
01:10
So let's stick all of this into our probability that we're looking for.
01:16
So we will say 5 choose 4 times 0 .76 to the 4th.
01:22
That's the probability of 4 successes and 0 .24 to the 1.
01:27
So that's the probability of one failure...