A quiz consists of 10 multiple-choice questions, each with four 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").
Given the "tactic" of the student, what is P(R) and P(W)?
The answer given by the text is :
Explanation:
There are four possible answers and the student chooses one at random, and therefore:
P(R) = 1/4 = .25, and P(W) = 3/4 = .75
I do not understand how one can arrive at this answer. Where did the .25 and .75 come from?