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Worksheet: Simulation in Statistics

Q1:

Anthony is designing a simulation to model the outcomes of the following game.

Each player drops a coin onto the target and receives the score corresponding to the color the coin lands on.

Assume the coin always lands somewhere on the target. Complete the table to determine the probabilities of landing on each color.

Section Blue (10 Points) Pink (25 Points) Green (50 Points) Orange (100 Points)
Probability
  • A 4 2 5 , 7 2 5 , 5 2 5 , 9 2 5
  • B 2 3 7 , 5 3 7 , 1 0 3 7 , 2 0 3 7
  • C 2 0 3 7 , 5 3 7 , 1 0 3 7 , 2 3 7
  • D 9 2 5 , 7 2 5 , 5 2 5 , 4 2 5
  • E 1 0 2 5 , 7 2 5 , 3 2 5 , 5 2 5

He wants to use a random number generator to simulate outcomes of the game. He will randomly generate integers between 0 and some number π‘₯ . Which of the following would be the best choice for π‘₯ ?

  • A24
  • B17
  • C3
  • D25
  • E13

He will perform 50 trials. Describe what a single trial will entail.

  • AA trial consists of generating a random number: a number between 0 and 3 will represent landing on orange, a number between 4 and 8 will represent landing on green, a number between 9 and 17 will represent landing on pink, and a number between 18 and 24 will represent landing on blue.
  • BA trial consists of generating a random number: a number between 0 and 5 will represent landing on orange, a number between 6 and 10 will represent landing on green, a number between 11 and 16 will represent landing on pink, and a number between 17 and 24 will represent landing on blue.
  • CA trial consists of generating a random number: a number between 0 and 3 will represent landing on orange, a number between 4 and 8 will represent landing on green, a number between 9 and 15 will represent landing on pink, and a number between 16 and 24 will represent landing on blue.
  • DA trial consists of generating a random number: a number between 0 and 2 will represent landing on orange, a number between 3 and 10 will represent landing on green, a number between 11 and 16 will represent landing on pink, and a number between 17 and 24 will represent landing on blue.
  • EA trial consists of generating a random number: a number between 0 and 4 will represent landing on orange, a number between 5 and 11 will represent landing on green, a number between 12 and 16 will represent landing on pink, and a number between 17 and 24 will represent landing on blue.

Q2:

William is designing a simulation to model the outcomes of rolling two dice and adding the numbers together.

He says that, in each trial, he can randomly generate a number between 2 and 12. This number will represent the sum of the numbers on the dice. Why is this incorrect?

  • AThis is because each die generates a number between 1 and 6.
  • BThis assumes that the experimental probabilities of each sum are the same.
  • CThis assumes that the theoretical probabilities of each sum are the same. When rolling two dice, the probabilities of each possible sum are not the same.

Q3:

Chloe is designing a simulation to model the ice cream sales at a local cafe.

Last week, 7 0 % of the ice creams sold were chocolate, 2 0 % were vanilla, and 1 0 % were strawberry.

She is going to use a spinner to generate data to predict this weeks sales. Which spinner should she use?

  • A
  • B
  • C
  • D

She will perform 50 trials. Describe what a single trial will entail.

  • AA trial consists of spinning the spinner once; landing on 𝐴 represents a customer choosing chocolate, landing on 𝐡 represents a customer choosing vanilla, and landing on 𝐢 represents a customer choosing strawberry.
  • BA trial consists of spinning the spinner once; landing on 𝐴 represents a customer choosing vanilla, landing on 𝐡 represents a customer choosing chocolate, and landing on 𝐢 represents a customer choosing strawberry.
  • CA trial consists of spinning the spinner once; landing on 𝐴 represents a customer choosing strawberry, landing on 𝐡 represents a customer choosing vanilla, and landing on 𝐢 represents a customer choosing chocolate.
  • DA trial consists of spinning the spinner once; landing on 𝐴 represents a customer choosing chocolate, landing on 𝐡 represents a customer choosing strawberry, and landing on 𝐢 represents a customer choosing vanilla.
  • EA trial consists of spinning the spinner once; landing on 𝐴 represents a customer choosing strawberry, landing on 𝐡 represents a customer choosing chocolate, and landing on 𝐢 represents a customer choosing vanilla.