00:01
For this exercise, we consider binomial distribution based on eight trials and probability of success .63.
00:12
Now the probability mass function for the binomial random variable is given by this formula.
00:34
And for part a we want the probability of exactly three successes.
00:39
This is the probability that x is equal to 3.
00:42
Using the probability mass function, we have 8 choose 3 times 0 .63 to the exponent 3 times 0 .37 to the exponent 5.
00:56
And this comes out to a probability of approximately 0 .03, 0 .097.
01:07
And for b, we want the probability of strictly less than 3 successes.
01:12
So this is the probability that x is smaller than 3, which is the probability that x is at most 2.
01:19
And so this is equal to the probability that x equals 0 plus the probability that x is equal to 1 plus the probability that x equals 2.
01:29
For x equals 0, the probability mass function simplifies to 0 .37 to the exponent 8.
01:36
And for x equals 1 we have the following.
01:46
And then for x equals 2 we have the following.
01:57
This comes out to approximately 0 .033, 034.
02:06
For c, we want the probability of at most 3 successes.
02:09
So let's use software to solve this one.
02:15
We can go to excel, and in excel we start a computation with an equal sign.
02:21
I want to use the binomial distribution function...