SOLUTION: *Below is the question I am trying to answer: A multiple-choice test has five questions, each with five choices for the answer. Only one of the choices is correct. You randomly gu

Question 792437: *Below is the question I am trying to answer:
A multiple-choice test has five questions, each with five choices for the answer. Only one of the choices is correct. You randomly guess the answer to each question. What is the probability that you answer the first two questions correctly?
*Below are the steps given:
Ans: (1/5)^2 *(4/5)^3 = 0.0205
*This is where I am confused. I am having trouble with setting this problem up, I would like to know the reasoning behind this setup for similar problems can you step me through the steps of how I should approach this problem? Please don't skip anything, I need to see "B" to get to "C".
Thank your help. This site really helps.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The probability that you answer each question correctly is .
The probability that you answer each question wrong is .
The probability that you answer each question correctly (or wrong) is independent of how the other questions were answered, so the probabilities are multiplied.
is the probability of answering just the first two questions correctly, and the other three questions wrong.

of the times you would have answered the first question correctly.
Out of those times, of them you would have answered the second question correctly.
That means of the times the first two questions would have been answered correctly. That is the probability of answering the first two questions correctly, not caring what happens with the third, fourth, and fifth questions.
The way the problem is worded, I would have thought that was the expected answer to the problem.

Out of the of the times the first two questions would be answered correctly, of those times you would get the third question wrong.
So of the times you would answer the first two questions correctly, and the third question wrong.
Out of those times, in of the cases, you would get the fourth question wrong.
So of the times you would answer the first two questions correctly, and the third and fourth questions wrong.
Out of those times, in of the cases, you would get the fifth question wrong.
So of the times you would answer the first two questions correctly, and the third, fourth and fifth questions wrong.
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