Probability Project

Probability Project Write-Up

Brooke (something) & Bryceeeee

June 6, 2018

Introduction

A spinner is often a way to display probability. In this game, called Twirl, players have an opportunity to win up to $12. This game is one that may be played at a carnival or an amusement park, as it holds potential to take money from consumers (negative expected value) or give the money back to the consumer (positive expected value). The entrance fee for Twirl is $3. In this game, the player simply spins the spinner once, and they are rewarded with the value displayed on the certain section of the spinner. For the negative expected value game, and the positive expected value game, if the player loses the game, (lands on a $0 section), they lose the $3 entry fee, resulting in a potential $3 loss. Along with the two $0 sections on the spinner, there is also one $5 section, which gives the player an opportunity to win $2. This would be considered winning the game, but there are three other options on the spinner that offer an even greater award. There are two $7 sections of the spinner. They are small, but these sections provide potential to win a net gain of $4. The last section, giving the grand total, offers $15, or a net gain of $12. So, in other words, losing the game results in a loss of $3, while winning the game can give the player up to $12 back. For the fair game, the player can either land on a $0 section, resulting in a $3 loss, or they can land on the $18 section, resulting in a $15 reward.

Instructions

Positive Expected Value

The player will step up to the game and will then pay the playing fee of $3. After this, they will have one chance to spin the spinner. There is a 48% chance they will land one of the two zero dollar sections. If the player is to land on one of these sections, they will walk away with no reward. If the player is to land on the $5 section, they will walk away with $5, resulting in a net gain of $2 which gives them a 32% chance of winning it. Landing in one of the two $7 sections will result in the player being rewarded $7, a net gain of $4. There is a 14% chance of the player landing in this section. Last, if the player is to land in the $15 section, they will walk away with $15, a net gain of $12. There is only a 6% chance of the player winning $15. With the expected value ending up to be $0.45.

Negative Expected Value

Just like the game with a positive expected value, the player will first pay $3 to play the game and have only one chance to spin the spinner. There is a 76% chance they will land one of the two $0 sections. If the player is to land on one of these sections, they will walk away with no reward, resulting in a $3 loss for the consumer. If the player is to land on the $5 section, they will walk away with $5, resulting in a net gain of $2. There is a 14% chance of the player winning $2. Landing in one of the two $7 sections will result in the player being rewarded a net gain of $4. There is a 8% chance of the player landing in this section. Last, if the player is to land in the $15 section, they will walk away with $15, a net gain of $12. There is only a 2% chance of the player winning $12. The expected value of the game is -$1.35.

Fair Expected Value

Similar to the previous games, the player has to pay $3 to play the game, and they have just one chance to spin the spinner. There is an 83.33% chance that they will land on one of the five zero sections. For the last section which they have a 16.67% of landing on to win the price of $18 dollars which gives them a net gain of $15. When calculated there is a fair expected value because if you played the game multiple times then you would expect to earn around $0.

there was also data tables with calculations