Overview
Hi,
Please reference the attached for instructions and book reference. Chosen question is highlighted.
No other information. Everything including the book you need to use is in the attachment. Please note I am unable to provide the book itself.
This assignment has two parts that contribute to the same assignment. I need to respond to three classmates posts.
Until I don't post my assignment I won't be able to see my classmates post. Classmate post 1:
I decided to play a carnival Ring Toss game, which costs $2.00 to play once. In this game, you toss a ring onto bottles to win a prize based on the color of the bottle you land on. There are 50 bottles in total, and the prizes and probabilities are as follows: a Red bottle (10% chance) wins a large prize worth $15.00; a Blue bottle (20% chance) wins a medium prize worth $8.00; a Green bottle (30% chance) wins a small prize worth $3.00; and a Yellow bottle (40% chance) wins a consolation prize worth $0.50.
To calculate the Expected Value, I find the net winnings for each outcome (Prize Value − $2.00 Cost) and multiply it by its probability. The calculation is:
.EV=(13×0.10)+(6×0.20)+(1×0.30)+(−1.50×0.40)
EV=1.30+1.20+0.30−0.60=2.20
Since the expected value is positive, I would, on average, expect to gain $2.20 each time I played this Ring Toss game.
Classmate post 2:
I chose the balloon dart game, where the goal is to pop a balloon to win a prize. The prize is a medium stuffed animal worth $20, and each throw costs $5. I estimated my chance of popping a balloon on a single throw is 1 in 6 (0.167 probability).
The expected value (EV) is calculated as:
EV = (Probability of Winning × Value of Prize) + (Probability of Losing × 0) EV = (0.167 × 20) + (0.833 × 0) EV = 3.34
Since I paid $5 per throw, the net expected value is: EV − Cost = 3.34 − 5 = −1.66.
This means that, on average, I lose $1.66 per throw, showing that carnival games are designed to favor the operator, even though there’s a small chance to win a prize.