if there is a multiple choice test of 9 questions. although only one answer is correct, there are four possible answers. what is the probability of a student getting all of the questions incorrect

Question

kirbykirby · Answer

What is the probability of getting one question incorrect? 

Then... for the second question, what is the probability of getting it incorrect??

Now, you can apply the product rule.. the probability of getting the 1st AND 2nd question incorrectly is... P(1st question incorrect) * P(2nd question incorrect)
----
Now apply this same logic for all 9 questions... apply the product rule for each individual question.

kirbykirby · Answer

(alternatively.. think of this as a Binomial distribution with 9 trials, and let $X$ be the the number of questions obtained incorrectly, then $X\sim Binomial (9, p)$ where $p$ is the probability of getting a question incorrectly. Thus, you find $P(X=9)$ )

perl · Answer

this is a binomial problem

perl · Answer

on any particular question, the probability of getting incorrect answer is 3/4 or 0.75 
Now apply this on 9 tests. then you have

perl · Answer

(3/4)^9 is the probability getting all incorrect