Dylan wants to form a chess club. His principal says that he can do that if Dylan can find six players, including him. How would you conduct a simulated model that estimates the probability that Dylan will find at least five other players to join the club if he asks eight players who have a 70% chance of agreeing to join the club? Suggest a simulation model for Dylan by describing how you would do the following parts.
1.Specify the device you want to use to simulate one person being asked.
2.What outcomes of the device would represent the person agreeing to be a member?
3. What constitutes a trial using your device in this problem?
4. What constitutes a success using your device in this problem?
5.Based on 50 trials, using the method you have suggested, how would you calculate the estimate for the probability that Dylan will be able to form a chess club?
To conduct a simulated model for estimating the probability that Dylan will find at least five other players to join his chess club, we can use the following steps:
1. Device to simulate one person being asked: We can use a random number generator (RNG) to simulate whether a person agrees to join or not. For example, we can use a function that generates a random number between 0 and 1, where any value below 0.7 represents agreeing to join and any value above 0.7 represents not agreeing to join.
2. Outcomes representing agreement: In this case, any outcome from the RNG less than 0.7 would represent a person agreeing to be a member of the chess club.
3. Trial: A trial would involve Dylan asking a specific group of eight players to join the chess club.
4. Success: A success would be when Dylan is able to find at least five players who agree to join the chess club.
5. Estimating the probability: To estimate the probability, we would perform multiple trials (let's say 50 trials). For each trial, Dylan randomly asks eight players, and we count the number of successes (finding at least five players who agree to join). The estimate for the probability would be the ratio of the number of successful trials to the total number of trials (in this case, 50).
For example, let's say out of 50 trials, Dylan successfully forms a chess club in 30 trials. The estimated probability would be 30/50 = 0.6, or 60%.
By repeating this simulation process with a larger number of trials, we can get a more accurate estimate for the probability that Dylan will be able to form a chess club.