Suppose the experimental probability is 1/3 that a carton of eggs contains at least one broken egg. Use the simulation of 20 trials to find the experimental probability that 3 cartons selected at random contain only unbroken eggs.
To find the experimental probability that 3 cartons selected at random contain only unbroken eggs using a simulation, you would follow these steps:
1. Set up the simulation: Generate a random number between 0 and 1 for each trial. If the random number is less than 1/3, consider it as a success (carton contains at least one broken egg), otherwise consider it a failure (carton contains only unbroken eggs).
2. Run the simulation: Repeat the simulation for a total of 20 trials. Keep track of the number of trials in which all 3 cartons contain only unbroken eggs.
3. Calculate the experimental probability: Divide the number of successful trials (all 3 cartons contain only unbroken eggs) by the total number of trials (20 in this case).
Let's work through the steps using the provided information.
Step 1: Set up the simulation
Generate a random number between 0 and 1 for each trial. If the random number is less than 1/3, consider it as a success (carton contains at least one broken egg), otherwise consider it a failure (carton contains only unbroken eggs).
Step 2: Run the simulation
Repeat the simulation for a total of 20 trials. Keep track of the number of trials in which all 3 cartons contain only unbroken eggs.
Here's an example of a simulation:
Trial 1: Success (random number < 1/3) => Failure
Trial 2: Failure (random number >= 1/3)
Trial 3: Failure (random number >= 1/3)
Trial 4: Success (random number < 1/3) => Failure
Trial 5: Failure (random number >= 1/3)
...
Trial 19: Failure (random number >= 1/3)
Trial 20: Success (random number < 1/3) => Failure
In this example, there are no successful trials where all 3 cartons contain only unbroken eggs.
Step 3: Calculate the experimental probability
Divide the number of successful trials (0 in this case) by the total number of trials (20).
Experimental probability = 0/20 = 0
Therefore, the experimental probability that 3 cartons selected at random contain only unbroken eggs, based on the simulation of 20 trials, is 0.