Hi, my name is Fatima Elmachatt,

I will be explaining how to do the problem number 23, here is the question:

A multiple-choice exam has 8 questions, and each question has 3 possible answers.If you guess the answer to each question and don’t leave any blank, what is the probability you get exactly 4 answers correct?

First: when am I am reading the problem I make sure that I read several times , to get what the question is really about and what kind of formula to use in order to solve it, so the key words for the problem are the ones I have highlighted , that reminds me of the:

 Binominal Formula: The Probability of getting exactly X success in a binominal experiment with trials is:

P(x)= nCx P^x q^n-x

In This case there are two possibility either I am going to guess the correct answer or the wrong one ,

Second: The probability of getting correct answer is 1/3 and the the probability of getting wrong answer is 2/3. (we have 3 possible answers)

Because when we give the right answer there is only one correct, when we pick other than the correct one, so there are 2 wrong ones, in this example.

Third: Now we can use our formula :

So here we are looking for the probability of getting exactly 4 answers correct, which the P(x).

The n is the number of the questions which is 8 questions.

The p is the probability of getting of getting one answer correct is (1/3)^4 , we are using the power 4 , because we want exactly 4 correct answers

The q letter corresponds to the wrong answer which is 1-1/3= (2/3) ^8-4

P(4)= 8C4*(1/3)^4*(2/3)^8-4

=70*0.012345679*0.197530864

  P(4) = 0.170705684

I hope that I explained the problem clear enough. Please don’t hesitate to ask for more details or further explanation, I will more than happy to help.