Is the probability 3/8 or 9/64 ?
The question reads out-
"There is a test consisting of 3 questions with 4 options each. Only one option is correct. A student guesses all 3 of them and gets exactly 2 right and one wrong. What is the probability of doing so?"
I reasoned this by the following method:
There are a total of 4*4*4=64 possible ways of answering.
There is only one way of getting an answer right, but three methods of getting a wrong answer. Total cases: 1*1*3*3 (for 3 questions)=9
Therefore probability is 9/64
However, our teacher told us to list the sample space
S={RRR,RRW,RWR,WRR,WWW,WWR,WRW,RWW}
There are 3 cases out of 8 in getting 2 answers right. So probability is 3/8.
Now, the question I wanted to ask is which one is correct? Because I feel that my method is more logical. Thanks.