Question 792437
The probability that you answer each question correctly is {{{(1/5)}}}.
The probability that you answer each question wrong is {{{(4/5)}}}.
The probability that you answer each question correctly (or wrong) is independent of how the other questions were answered,  so the probabilities are multiplied.
{{{(1/5)^2 *(4/5)^3 = 0.02048}}} is the probability of answering just the first two questions correctly, and the other three questions wrong.
 
{{{1/5}}} of the times you would have answered the first question correctly.
Out of those times, {{{1/5}}} of them you would have answered the second question correctly.
That means {{{(1/5)^2=0.04}}} 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 {{{(1/5)^2=0.04}}} of the times the first two questions would be answered correctly, {{{4/5}}} of those times you would get the third question wrong.
So {{{(1/5)^2 *(4/5)}}} of the times you would answer the first two questions correctly, and the third question wrong.
Out of those times, in {{{4/5}}} of the cases, you would get the fourth question wrong.
So {{{(1/5)^2 *(4/5)*(4/5)=(1/5)^2 *(4/5)^2}}} of the times you would answer the first two questions correctly, and the third and fourth questions wrong.
Out of those times, in {{{4/5}}} of the cases, you would get the fifth question wrong.
So {{{(1/5)^2 *(4/5)^3}}} of the times you would answer the first two questions correctly, and the third, fourth and fifth questions wrong.