What is the probability of having 3 good answers

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Imagine that you have not studied for this midterm. There are 10 multiple-choice questions and for each of these questions there are 4 possible choices (for example, the correct answer is a, b, c, or d). You decide to answer these 10 questions in a purely random way, assuming that each of the options (a, b, c, and d) has the same probability of being the correct answer.

a) What is the probability of having 3 good answers out of 10?

b) What grade should you expect if you answer these 10 questions randomly assuming you have two points per correct answer and 0 per wrong answer?

c) What would be the variance of the score if you answer these 10 questions randomly, assuming you have two points per correct answer and 0 per wrong answer?

Reference no: EM132401543

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