Liang wants to form a chess club. His principal says that he can do that if Liang can find six players, including him. How would you conduct a simulated model that estimates the probability that Liang 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 Ling 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 Liang will be able to form a chess club?
1. To simulate one person being asked, I would use a random number generator. The random number generator will generate a number between 0 and 1, and I will set a threshold for accepting or rejecting the invitation based on this random number.
2. If the generated random number is less than or equal to 0.7, it would represent the person agreeing to be a member.
3. A trial in this problem would involve asking eight players and recording how many of them agree to join the club.
4. A success in this problem would be if Liang finds at least five other players who agree to join the club.
5. To estimate the probability, we can perform 50 trials using the simulation model. In each trial, we ask eight players with a 70% chance of agreeing. We record the number of players who agree in each trial and count the number of trials where there are at least five players who agree. The estimate for the probability that Liang will be able to form a chess club is then calculated by dividing the number of successful trials by the total number of trials (50 in this case).
To conduct a simulated model that estimates the probability of Liang finding at least five other players to join his chess club, we can follow these steps:
1. Specify the device you want to use to simulate one person being asked:
We can use a random number generator or dice to simulate whether a person agrees to join the chess club or not. We will assume that each person has a 70% chance of agreeing to join.
2. Determine the outcomes of the device that represent a person agreeing to be a member:
Let's assume that rolling a number between 1 and 7 (inclusive) on a six-sided die or getting a random number between 1 and 10 from a random number generator represents the person agreeing to join the chess club. Any other outcome would imply that the person declined.
3. Define a trial using your device in this problem:
A trial in this simulation would consist of asking eight players to join the chess club using the method specified in Step 1. Each trial aims to find out how many players agree to join.
4. Determine a success using your device in this problem:
In this problem, a success is defined as finding at least five other players who agree to join the chess club, including Liang himself.
5. Calculate the estimate for the probability based on 50 trials using the suggested method:
To estimate the probability of forming a chess club, we would perform 50 trials using the device described in Steps 1 and 2. In each trial, we would count the number of players who agreed to join the club (including Liang) and note whether it meets the success criteria explained in Step 4. By dividing the number of successful trials by the total number of trials (50 in this case), we can calculate an estimate for the probability that Liang will be able to form the chess club.