00:01
This question is about the binomial random variable and binomial probability.
00:05
So first of all, let's recall what is this binomial probability.
00:08
So in binomial probability, we need the probability of success.
00:12
And we need the number of trial, which is denoted by this is number of trial.
00:18
And this is probability of success.
00:22
And we can just define the random variable for this binomial distribution.
00:25
This is n and p.
00:27
And the formula for this one, which is x is equal to lowercase s, this is nx combination times p to the power x times q to the power n minus x.
00:38
And what is q here? so the q is equal to 1 minus p.
00:42
This is the rule we have to apply for this question.
00:46
So for part a, what is given? let me just take notes.
00:50
So the n value is given as 5 and the probability of the success that was given as 0 .6.
00:56
So what we defined, x is less than or equal to 4.
01:00
So we have to find x is less than or equal to four.
01:03
So what that means, we have to just find the probability of when x is equal to zero, when x is equal to 1, when x is equal to 2, and when x is equal to 3, and when x is equal to 4.
01:16
So it is very complicated to find each of them separately.
01:20
Instead of doing this operation here, we can just use the binom cdf function for the graphing display calculator.
01:27
So we can use the binom cdf.
01:29
What we are going to put, we're going to put the number of trial, which is 5 and the probability of success, and the x, which is included value here, which is 4.
01:38
So i'm going to just press the button second and variance.
01:41
So we have the binaum cdf at the bottom of the page here.
01:44
This is binom cdf.
01:46
So the end value here is 5, and the probability of success is 0 .6, and then we have 4.
01:53
So the answer would be this is 0 .92, let's say, 22.
01:57
So this is the answer for part a.
02:01
What about for part b? for part b, it says, again, the n value is given as 5, but in this case, the probability was given as 0 .7 here.
02:14
So we need to find the probability of the random variable x, which is greater than 1.
02:20
So greater than 1.
02:22
That means.
02:23
So which is not included here.
02:26
So actually that means when x is equal to 2, when x is equal to 3, and when x is equal to 4, and then when x is equal to 5.
02:35
We can just get this value.
02:37
Or practically, we can just find this one.
02:39
This is 1 minus the excluded part here, which is the x is less than or equal to 1, which means this is 1 minus the probability of x is equal to 0, plus the probability of x is equal to 1...