00:01
Hey there, welcome to numerating.
00:02
Let's start with part a over here in which we're trying to find the probability of five successes with the probability of success is 0 .55.
00:12
So before we dive in, we're going to write the binomial equation, the probability of x equals combinations and choose x times the probability raised to the x times the complement raised to the n minus x.
00:29
So for for the probability of 5 successes, we are going to plug this in.
00:35
Probability 5 is equivalent to, we have 20 choose 5 times 0 .55 raised to the 5th multiplied by the complement raised to 20 minus 5 equals 15.
00:54
Hence, this gives us an answer here for part a equaling 0 .0049.
01:03
Now for part b, we're looking for the probability that we have at least 7 successes.
01:09
So we know this is equivalent to the probability of 7 added to, so let's see here, probability of success will be 0 .2, whereas sample size will be 20.
01:21
So, hence this is going to be probability 7 plus the probability 8, going upwards since we have at least, and this is going to be all the way up to the probability of 20.
01:35
So, knowing this, we're going to plug each one of this into the equation above, giving us a probability that equals around 0 .0867...