Suppose Artemis is considering whether or not to enter an ar

Suppose Artemis is considering whether or not to enter an archery contest. The entry fee is $15. Contestants get 1-shot at a target, if they get the bulls-eye they get $100, if they hit the target but do not get a bulls-eye they get $10 and if they miss completely they get nothing. She has a 5% chance of getting a bulls-eye and a 40% chance of missing completely. According to the expected value rule, should she enter the contest? What would a fair entry fee be for Artemis?

Solution

A denote artemis hits blue eye

B denote she completely miss the target

C denote she hits the target but not bull eye

so

P(A)=0.05   P(B)=0.40   P(C)=0.55

so expectated price =100*0.05+0*0.44+0.55*10=5+5.5=11.5

by expected value rule she does not enter the contest.

if the entry fee is equal to $11.5 then it is fair for artemis