A baseball team averages one win to every one loss. Use a simulation to find each experimental probability for three games.

P(1 win and 2 losses) and P(three losses)

The more simulations you run, the closer the experimental probabilities will be to the theoretical probabilities.

To calculate the experimental probability, we can use a simulation where we simulate multiple sets of three games and count the number of times the desired outcomes occur.

Here's how we can calculate the experimental probability for each case:

P(1 win and 2 losses):

Simulate a large number of sets of three games (e.g., 10,000).

For each set, randomly assign a win or a loss for each game based on the average of one win to every one loss.

Count the number of sets where there is exactly one win and two losses.

Divide the count by the total number of sets (10,000) to get the experimental probability.

P(three losses):

Simulate a large number of sets of three games (e.g., 10,000).

For each set, randomly assign a win or a loss for each game based on the average of one win to every one loss.

Count the number of sets where there are three losses.

Divide the count by the total number of sets (10,000) to get the experimental probability.

Note: The above method assumes that the probability of winning or losing each game is equal (i.e., 0.5 for each).

Here's an example of how the calculations can be performed using a simulation:

P(1 win and 2 losses):

Simulate 10,000 sets of three games.

Count the number of sets with exactly one win and two losses.

Let's say the count is 4,100.

Experimental probability = 4,100 / 10,000 = 0.41

P(three losses):

Simulate 10,000 sets of three games.

Count the number of sets with three losses.

Let's say the count is 5,200.

Experimental probability = 5,200 / 10,000 = 0.52

Remember, the experimental probabilities obtained through simulations may vary slightly due to the random nature of the simulation.

The more simulations you run, the closer the experimental probabilities will be to the theoretical probabilities.

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