You and five of your friends like to go to McDonalds once a week and get Happy Meals for the prize inside. McDonalds has just started a new “dinosaur toy” promotion for their Happy Meals with six different dinosaurs you can collect: Brachiosaurus, Brontosaurus, Diplodocus, Tyrannosaurus, Plesiosaurus, and Allosaurus. You each want to collect at least one of all six dinosaurs, but the prizes are randomly placed in Happy Meals, and there is no way to know which dinosaur you’re getting until you open the Happy Meal bag.
How might you design a simulation experiment to find the likelihood (experimental probability) of getting all six toys after one, two, three, etc. weeks?
generate random numbers from 1 to 6. (Roll a die)
Roll the die 100 times or so and see what happens. Then analyze your results.
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To design a simulation experiment to find the likelihood of getting all six toys after a certain number of weeks, you can follow these steps:
1. Define the variables: First, you need to define the variables that will be involved in your simulation. In this case, the important variables are the number of weeks and the number of Happy Meals purchased each week.
2. Determine the sample space: The sample space refers to all the possible outcomes of your simulation. In this scenario, the sample space would comprise the different combinations of dinosaurs that can be obtained over multiple weeks.
3. Set the initial conditions: Start by assuming that no one has any dinosaur toys. Initialize a count for each dinosaur toy set to zero.
4. Simulate the Happy Meal purchases: Repeat the following steps for the desired number of weeks:
a. Purchase the specified number of Happy Meals: Use a random number generator to determine the number of each dinosaur toy received in each Happy Meal.
b. Update the count of each dinosaur toy: Increment the count of each dinosaur toy based on the toys received in the Happy Meals purchased.
c. Check if all six toys have been collected: After each week's purchases, check if all six dinosaur toys have been collected. If yes, stop the simulation and record the number of weeks it took to collect all the toys.
5. Repeat the simulation multiple times: To obtain a reliable estimate of the likelihood, repeat the simulation a sufficient number of times, such as 1000 or 10,000 iterations.
6. Calculate the experimental probability: Finally, calculate the experimental probability by dividing the number of successful outcomes (all six toys collected) by the total number of simulations performed.
By following this simulation experiment design, you can estimate the likelihood of collecting all six dinosaur toys after different numbers of weeks based on the simulated outcomes.