you can a summer fair event at which one of the booths is skee-ball Problem 2 (1

Question

you can a summer fair event at which one of the booths is skee-ball Problem 2 (10 points).You attend a summer fair event at which one of the booths is the game "Skee-Balr. For $2, you can purchase 3 balls and have 3 opportunities to roll each ball into a centrally located target You will receive your $2 back and win an additional $1 if you hit the target once, an additional $3 if you hit the target twice and an additional $S if you hit the target three times. If you do not hit the target at all, you will lose your initial $2. has a 20% probability of hitting the target on each roll. In the long run, would The average player the average player expect Skee-Ball to be a profitable game? If not, how much can the average Skee-Ball player expect to lose on each game? a) Suppose you are a particularly good Skee-Ball player and you have a 50% probability of hitting the target on each roll. How much can you expect to win on each game? b)

Explanation / Answer

In this game the payoffs given is as below

for 1 hit = (2+1)=3$

for 2 hit = (2+1+3)=6$

For all 3 hit = (2+1+3+5)=11$

While for no hit =0

The cost associated with the game is 2$

Now since we know the payoffs we can easily solve the problems

(a) so on each turn an avg player has a 20% probability to hit

So the payoff here will be = -2 + [0.2*(3) + 0.2*0.2*(6) +0.2*0.2*0.2*(11)] =-2+0.928=-1.072 [i.e. -cost+Payoff at 1 hit * probability + Payoff at 2 hit * probability of 2 consecutive hits +Payoff at 3 hit * probability of 3 consecutive hits]

Since we can see from the above that on an avg an avg player has a payoff of -1.072$ from the game and so we can say that an avg player can never earn from this game who has a prob of 20% hitting the aim

b) Since now the prob has been changed to 50% from 20% since it says that you are goog at aiming and so the payoffs for you will be

=-2 + [0.5*(3) + 0.5*0.5*(6) +0.5*0.5*0.5*(11)] =-2+4.375=2.375 which is quite good profit(Approximately 118.75%)

So in this case it's a favourable situation and you can expect to earn 2.375$ from each game.

Hope this has helped you in understanding the problem. Pls upvote the ans if it has really helped you. Good Luck!!

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