00:01
In this question, we are given a 10 multiple choice questions exam and probability of choosing a correct answer by knowledgeable guessing is 0 .4.
00:09
Now, a student makes knowledgeable guesses to all questions, and i'm going to let x be the number of correct answers out of 10 questions answered by knowledgeable guessing.
00:19
Now, x actually follows the binomial distribution.
00:21
You can see there are four criteria to this distribution.
00:25
The first criteria, the number of trials end is fixed at analytical.
00:28
In this case, there are 10 questions, so there will be 10 trials, so n equals to 10.
00:33
In each trial, we're looking at the question whether it's being answered correctly or not, so the 10 trials are identical, hence the first criteria is fulfilled.
00:41
The second criteria, each trial is independent, so each question whether they are answered correctly or not, is independent of the other questions.
00:49
So the second criteria is fulfilled.
00:51
The third criteria, each trial results in order to outcomes, success and failure.
00:55
So in each question, the success is answered correct.
00:58
The failure is not answered correctly.
01:01
So the criteria 3 is fulfilled.
01:03
The last criteria probability of success in single trial, denoted by p, remains the same from trial to trial.
01:10
So this means it's the probability of a question may answer correctly and that will be 0 .4...