Probability solved with expected value E(X)

[ParisSpart]

A question on a multiple choice test has 6 answers which just one is right and the other wrong.

If the amount of the correct answer is 10 points how many points should be substracted for a wrong answer so if nobody answers randomly choosing one of the 6 answers get, on average, 0 points?



i thinh that this problem can be solved with expected value E(X) but i am confused on how to do it
maybe this E(X)=10*(1/6)+0*(1/6)?

 

[HallsofIvy]

Your "E(X)= 10*(1/6)+ 0(1/6) is almost right but: you have "0" right where you want your unknown- the number of points given for a wrong answer and the probability of a wrong answer is 5/6, not 1/6. And you want the expected value to be 0: 10(1/6)+ x(5/6)= 0. Solve that for x.