Solution: 2013 Fall Midterm - 17

Author: Pat Morin

Question

If you answer each question in this midterm by choosing an answer uniformly at random, what is the probability that you get all answers correct?

(a)

$1/4^{17}$

(b)

$4^{17}/3^{17}$

(c)

$3^{17}/4^{17}$

(d)

$1/17^{4}$

Let A be the event that we get a question correct

We have 4 options and only one of them is correct $ \Pr(A) = \frac{1}{4} $

We’re basically trying to replicate this success 17 times:

$ \Pr(A) \cdot \Pr(A) \cdot \ldots \cdot \Pr(A) = \frac{1}{4} \cdot \frac{1}{4} \cdot … \cdot \frac{1}{4} $

The probability of getting all 17 questions correct is $ \frac{1}{4^{17}} $