Sure! Let's go through the steps to determine the experimental probabilities of getting heads (H) or tails (T) after flipping a coin 200 times.
### Step-by-Step Solution:
#### Step 1: Understand the Setup
We aim to determine the probabilities of obtaining heads (H) or tails (T) after flipping a coin 200 times.
#### Step 2: Perform the Experiment
You need to flip the coin 200 times. For each flip, you record the outcome, either heads (H) or tails (T).
Here are the outcomes after 200 flips based on the given data:
- Heads (H): 109 times
- Tails (T): 91 times
#### Step 3: Calculate the Experimental Probability
To calculate the probability of an event [tex]\(E\)[/tex], you use the formula:
[tex]\[
P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}}
\][/tex]
In this context, we have:
- Total number of trials (flips): 200
Let's calculate the probabilities for both heads and tails.
#### Step 4: Calculate the Probability of Heads (H)
To find the probability of getting heads:
[tex]\[
P(H) = \frac{\text{Number of times heads occurs}}{\text{Total number of flips}} = \frac{109}{200} = 0.545
\][/tex]
So, the experimental probability of obtaining heads (H) is [tex]\(0.545\)[/tex].
#### Step 5: Calculate the Probability of Tails (T)
To find the probability of getting tails:
[tex]\[
P(T) = \frac{\text{Number of times tails occurs}}{\text{Total number of flips}} = \frac{91}{200} = 0.455
\][/tex]
So, the experimental probability of obtaining tails (T) is [tex]\(0.455\)[/tex].
### Summary of Results:
- Number of Heads (H): 109
- Number of Tails (T): 91
- Probability of Heads (H): 0.545
- Probability of Tails (T): 0.455
By following these steps, you can determine the experimental probabilities of obtaining heads and tails from the given experimental data.
