The question itself is:
A carnival Sharpshooter game charges $25 for 25 shots at a target. If the shooter hits the bullseye fewer than 5 times then he gets no prize. If he hits the bullseye 5 times he gets back $10. For each additional bullseye over 5 he gets back an additional $5. The shooter estimates that he has a .2 probability of hitting the bullseye on any given shot. What is the shooter's expected gain if he plays the game (nearest $1)?
In the answer, they make a table for # of bullseye, Prize corresponding to that, and for 5X - 15, X is # of bullseyes. I don't understand where they get 5X-15 from, and then why they "adjust factors for X = 0,1,2,3,4" as they say.
A carnival Sharpshooter game charges $25 for 25 shots at a target. If the shooter hits the bullseye fewer than 5 times then he gets no prize. If he hits the bullseye 5 times he gets back $10. For each additional bullseye over 5 he gets back an additional $5. The shooter estimates that he has a .2 probability of hitting the bullseye on any given shot. What is the shooter's expected gain if he plays the game (nearest $1)?
In the answer, they make a table for # of bullseye, Prize corresponding to that, and for 5X - 15, X is # of bullseyes. I don't understand where they get 5X-15 from, and then why they "adjust factors for X = 0,1,2,3,4" as they say.
ACTEX question on Expected gain from a game
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