00:01
A quiz has 10 multiple choice questions.
00:03
So i've got n equals 10.
00:04
Each question has five answers.
00:06
One is correct.
00:07
Correct answer is eight points and incorrect answer is minus two points.
00:12
They are answered completely at random.
00:14
So it's fair for me to consider each of these independent of each other.
00:18
Whatever happens on one question won't influence the others.
00:22
Okay, so how could we simulate the student's total score? okay, so we could have a box containing these tickets.
00:35
We would have minus two for an incorrect answer, minus two for an incorrect answer, and so on and so on, and then finally eight for a correct answer.
00:44
And if you pick one of these at random, you've simulated guessing on one of the questions.
00:50
And then you replace the tickets because they are independent.
00:55
You need to return to the previous setup and repeat 10 times.
01:02
Repeat 10 times, adding tickets, and you would end up with a score.
01:11
So that's how you could simulate it.
01:13
The key is to make sure that the probabilities work out.
01:16
The probability of getting a question correct is one in five, 0 .2.
01:20
And that works here.
01:22
One correct ticket, four incorrect ones.
01:25
And they have the correct values to match up to the actual outcomes of getting one correct or getting one wrong.
01:33
Ok, now what score is expected? ok, so we're looking basically for the expected value or the mean.
01:41
To get the expected value of a distribution, take each possible outcome, multiply it by the probability of occurring and add them up...