00:01
Here we have a 10 question, multiple choice test, and for each question there are four possible solutions.
00:10
Someone is just randomly guessing at all the answers.
00:13
So for an individual question, the probability of guessing it correct is 1 out of 4 or 0 .25.
00:20
We want to find the probability of passing the test.
00:23
That is the probability of scoring at least 50 % if randomly guessing.
00:28
So let's define a random variable x as the number of questions guessed correctly.
00:44
Each question can be seen as a bernoulli trial, which has only two possible outcomes, success or failure.
00:51
And since the student is randomly guessing, we can say that each question is independent from the other questions.
00:58
That is the outcome for each question is independent from the outcomes for the other nine questions.
01:03
The number of successes in a given number of independent bernoulli trials is a binomial random variable.
01:13
So here x is a binomial random variable.
01:22
Now if a pass is scoring at least 55%, and since it's multiple choice you can only get full marks or zero marks for each question, this means that we must get at least six questions correct because five questions correct would not pass...