Sina Ghaffarnejad
P1
10/1/2014
Math Write-Up For Rug Games
Problem Statement: Imagine that each diagram in this activity represents a rug. A trap door opens down, landing at random somewhere on the rug. At random means that every point on the rug has a good chance of getting hit as every other point.
Process: The process that I took to solving this problem was to take the image and chop it up into smaller pieces so it would simplify turning it into a fractional problem. I then counted how many of the pieces are shaded grey and how many are white. I then place those numbers as the numerators and the total numbers of pieces would be the denominator.
P1
10/1/2014
Math Write-Up For Rug Games
Problem Statement: Imagine that each diagram in this activity represents a rug. A trap door opens down, landing at random somewhere on the rug. At random means that every point on the rug has a good chance of getting hit as every other point.
Process: The process that I took to solving this problem was to take the image and chop it up into smaller pieces so it would simplify turning it into a fractional problem. I then counted how many of the pieces are shaded grey and how many are white. I then place those numbers as the numerators and the total numbers of pieces would be the denominator.
many of the pieces are shaded grey and how many are white. I then place those numbers as the numerators and the total numbers of pieces would be the denominator.
Solution: I will exemplify my solution with the work that I had done.
The probability for landing on grey is 7/12.
The probability for landing on white is 5/12
If you divide the numerator by the denominator you will find the percentage for the probability.
Grey= 12/7 = 58% That means that grey has a 58% chance to be landed on.
White= 12/5= 42% That means that grey has a 42% chance to be landed on.
Extension: There are many extensions that we can do and processed to make this problem more difficult and challenging. They will become more difficult by including factors of things such as weighted probability and theoretical probability. What we can use the weighted probability for in this problem is to add a third party factor that will impact the results of the problem and maybe can change it from a problem to a actual game.
The Problem: You use the same rugs with the same amount of squares all colored the same color. Virtually you will change nothing, just add things. The thing that you will add is value to the boxes.
say that you have two players playing, Jack and Sam. Jack bets Sam that whenever the object lands on grey, Sam has to play him 5 dollars buts whenever the object lands on white, Jack will pay Sam 7 dollars. Find out who would have the most money at the end of 12 trials.
The Answer:
Its probable that the object will land on grey 7 times out of 12 based off theoretical probability
Its probable that the object will land on white 5 times out of 12 based off theoretical probability
If Jack gets 5 dollars every time the object lands on grey then he would have $35(5x7=35)
If Sam gets 7 dollars every time the object lands on white then he would have $35(7x5=35)
Jack and Sam will probably both have made the same amount of cash.
Solution: I will exemplify my solution with the work that I had done.
The probability for landing on grey is 7/12.
The probability for landing on white is 5/12
If you divide the numerator by the denominator you will find the percentage for the probability.
Grey= 12/7 = 58% That means that grey has a 58% chance to be landed on.
White= 12/5= 42% That means that grey has a 42% chance to be landed on.
Extension: There are many extensions that we can do and processed to make this problem more difficult and challenging. They will become more difficult by including factors of things such as weighted probability and theoretical probability. What we can use the weighted probability for in this problem is to add a third party factor that will impact the results of the problem and maybe can change it from a problem to a actual game.
The Problem: You use the same rugs with the same amount of squares all colored the same color. Virtually you will change nothing, just add things. The thing that you will add is value to the boxes.
say that you have two players playing, Jack and Sam. Jack bets Sam that whenever the object lands on grey, Sam has to play him 5 dollars buts whenever the object lands on white, Jack will pay Sam 7 dollars. Find out who would have the most money at the end of 12 trials.
The Answer:
Its probable that the object will land on grey 7 times out of 12 based off theoretical probability
Its probable that the object will land on white 5 times out of 12 based off theoretical probability
If Jack gets 5 dollars every time the object lands on grey then he would have $35(5x7=35)
If Sam gets 7 dollars every time the object lands on white then he would have $35(7x5=35)
Jack and Sam will probably both have made the same amount of cash.