# Probability Question Dealing With Multiple Choice Questions

A students is taking a multiple choice test where each question has 5 possible answers, only one of which is correct. If the student knows the answer he selects the correct answer, otherwise he selects his answer choice randomly. The student knows the answer to $$70$$% of the questions.

i) What is the probability that on a given question, the student gets the correct answer?

My thought was that I could use conditional probability:

$$\dfrac{(0.2)(0.7)}{0.2}$$

But then thought maybe that would not be appropriate, and a made a tree diagram and came up with an answer of $$0.76$$. This takes into account, I believe, the cases where he does not know the answer but guesses correctly.

Any thoughts?

• The answer of $.76$ is correct, you can see it as $.7\times 1 +.3\times .2$ – lulu Jun 2 '19 at 16:29

$$P($$ correct $$) = P($$ know $$)+ ( P$$ guesses$$)$$
$$=0.7 \times 1 + 0.3 \times \frac{1}{5}$$
Hence required probablilty is $$0.76$$