Probability theory
 

Friends, I urgently need to solve the problem I received on probability theory.

A class is taking a multiple choice test with 10 questions where each question has four possible answers. Assume that the answer to any question is independent of that to any other answer. Robert has forgotten to study for this test, so he simply guesses for each question.
What is the probability that Robert guesses exactly 8 of the questions correctly? (Round to four decimal places.)
What is the probability that Robert gets an
or better? Another way of saying this is, what is the probability that he guesses 8 or more questions correctly? This would be the probability of 8 plus the probability of 9 plus the probability of 10. (Round to four decimal places.)

At [removed] I got some answers, but did not fully understand the logic of solving the problem . I will be very grateful for your explanation.

Show us what you got so far, we'll take it from there.

The probability of getting all of the questions wrong is 0.75 times 0.75 times 0.75....in short 0.75 to the power of ten.

So the probability of getting at least one or more questions correct is 1 minus (0.75 to the power of ten).

I am not sure, but the probability of getting exactly eight questions correct could be (0.25 to the power of eight) times (0.75 to the power of two).

Don't blame me if you give the wrong answer for your homework.

Could it be done with GNUPLOT?

Gnuplot is ultimate tool for maths. R for stats.