A quiz consists of 10 multiple-choice questions, each with 4 possible answers, only one of which is correct. A student who does not attend lectures on a regular basis has no clue what the answers are, and therefore uses an independent random guess to answer each of the 10 questions. What is the probability that the student gets at least one question right?

Let's decide on some notations.

Let L be the event that the student gets at least one of the questions right.

We'll use R for getting a question right and W for getting it wrong (W is essentially "not R").

1. Given the "tactic" of the student, what is P(R) and P(W)?

2. Since L is an event of the type "at least one", it is much easier to find P(not L) and then use the Complement Rule.

P(L) = 1 - P(not L).

Write in words what the event "not L" is, and then find P(not L) using the multiplication rule.

3. Now, complete the problem by finding P(L)