Given that the student gets the correct answer to this, Basic Statistics

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Given that the student gets the correct answer to this

Question: A student takes a multiple choice examination where each question has 5 possible answers. He works a question correctly if he knows the answer, otherwise he guesses at random, Suppose he knows the answer to 70% of the questions.

a) What is the probability that on a question chose at random the student gets the correct answer?

b) Given that the student gets the correct answer to this question chosen at random, what is the probability that he actually knew the answer? Suppose there are 20 questions on the examination, Let N be the number of questions that the student gets correct.

c) Find E(N).

d) Find SD(N).

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