suppose the experimental probability is 1/3 that a carton of eggs contains at least one broken egg. Use a stimulation of 20 trials to find the experimental probability that three cartons selected at random contain only unbroken eggs.
To find the experimental probability that three cartons selected at random contain only unbroken eggs, we can use a stimulation of 20 trials. Each trial represents randomly selecting three cartons and checking if they contain only unbroken eggs.
Here's how you can perform the stimulation:
1. Start by setting the initial count of successful trials (containing only unbroken eggs) to zero.
2. Repeat the following steps 20 times:
a. Randomly select three cartons.
b. Check if all three cartons contain only unbroken eggs. If yes, increase the count of successful trials by one.
3. After completing all 20 trials, divide the count of successful trials by 20 to get the experimental probability.
Let's go through an example simulation:
Step 1: Set the initial count of successful trials to zero.
Step 2:
- Trial 1: Randomly select three cartons and check if they contain only unbroken eggs. Suppose we find that they do contain only unbroken eggs, so increase the count of successful trials to one.
- Trial 2: Randomly select three cartons and check if they contain only unbroken eggs. Suppose we find that they don't contain only unbroken eggs, so keep the count of successful trials at one.
- Continue this process for the remaining trials, checking if each trial contains only unbroken eggs.
Step 3:
- After completing all 20 trials, if the count of successful trials is, for example, six, then the experimental probability would be 6/20, which simplifies to 3/10.
By performing this stimulation and counting the number of times three cartons contain only unbroken eggs, you can calculate the experimental probability.