00:01
Here in this problem, we are told, that we have a binomial distribution, the p value is 0 .7, and the n value is 18.
00:08
And we want to find a couple of different probabilities here.
00:12
First thing we were looking for is the probability that the number of successes is equal to 12.
00:18
Now, because this is a binomial, that means the probability of x is in choose x, so 18 choose x, times p to the x, 0 .7 to the x, times 1 minus p to the n minus x, so 0 .3 to the 18 minus x.
00:38
Probability of 12 would be 18 choose 12 times 0 .7 of the 12 times 0 .3 to the 18 minus 12, so to the 6 power.
00:52
Now from here we can just type this in exactly like it looks on our calculator.
00:56
At 18 choose 12 is just the ncr button, so you do 18 ncr 12.
01:01
And when we evaluate this, this gives us 0 .1873.
01:06
And so our probability is 0 .1873...