Mary takes a multiple-choice quiz of four questions that are administered on a clicker in class. Each question has four possible answers (three wrong, one right). Assume the questions are independent of each other.

What is the probability that she answers correctly if she is giving a random guess? What is the probability that she is wrong in a random guess?

Draw out the sample space for the four questions using R to stand for Right and W to stand for Wrong for the outcome for each question. For example, for four correct guesses there is one way for this to happen and it would be represented as R R R R.

The probability for this is .25*.25*.25*.25 = .25^4 = .0039063.

Drawing out the sample space takes a bit of doing, but it is manageable. Excel would be very good for drawing this out and calculating the probabilities. Hint: There are 16 different combinations for the sample space.

What is the probability that she answers only one question correctly? (Hint: identify all the possible ways to get 1 right).

What is the probability that she gets all four questions right?

What is the probability that she gets all four questions wrong?

What is the probability that she gets 2 questions correct?