00:01
In this question, we are given an experiment of repeatedly rolling a six -sided die.
00:07
Now, which of the following is a binomial random variable? now, before we do that, let's look at the criterials for a binomial distribution.
00:15
There are four criteria.
00:17
First criteria, the number of trials and is fixed are identical.
00:21
So the experiment has a fixed number, and each of this experiment are identical.
00:29
Criteria 2, each trial is independent.
00:33
Criterary 3, each trial results in one or two outcomes, success and failure.
00:39
Criteria 4, the probability of success, denoted by p, remains the same from trial to trial.
00:45
That means every trial, the probability of success is the same.
00:50
So let's look at the first statement here, the number of roles that wrote at least of 4.
00:57
Now, in this case, for the first option here, if i were to let x be the number of rows out of n rows is at least a 4.
01:24
This fits the binomial distribution criteria because first of all, the number of trials n is fixed and all are identical as in every trial we are looking at whether we get at least a 4.
01:44
Second criteria, each trial is independent.
01:47
So these end roles are n trials and they are all independent, so that is correct.
01:52
The criteria each trial results in one to outcome success and failure.
01:56
So for each of this role, success is we get at least a four.
02:00
The failure is we do not get at least a four.
02:04
So third criteria is fulfilled.
02:06
Now fourth criteria, probability of success remains the same from trial to trial.
02:10
In this case, probability of success in a single trial will be getting at least a 4...