Trigonometry probability problem, please show all works instead of only answers

Question

suppose that you are taking your college board tests. you answer all the questions you can, and have some time left over, so you decide to guess at the answer to the rest of the questions.

a. each question is multiple choice with 5 choices. if you guess at random, what is the probability of getting an answer right?

b. what is the probability of getting an answer wrong?

c. when educational testing service grades your paper, they give you 1 point if the answer is right, and subtract 1/4 point if the answer is wrong. what is your mathematically expected score on any question for which you guess at random?

d. suppose you can eliminate two of the choices you know are wrong, and you randomly guess among the other three. what is you mathematically expected score on the question?

e. if you can eliminate three choices, and ra dolly guess between the other two, what is your mathematically expected score?

f. based on your answers, is it really worthwhile guessing answers on a multiple choice test?

please show all works instead of only answers

Answer 1

a> 1/5

b> 4/5

c>1/5*1 - 4/5*(1/4) = 0

d> 1/3*1 - 2/3*(1/4) = 1/6

e> 1/2*1 - 1/2*(1/4) = 3/8

f> you answer this one!