Answer :
Let's break down the problem step by step in order to determine which statement about the coin flipping experiment is correct.
### Step 1: Understanding the Experiment
Mai flipped a fair coin 200 times, and it landed heads up 110 times.
### Step 2: Calculating the Experimental Probability
The experimental probability is given by the number of times the event occurred divided by the total number of trials. In this case:
[tex]\[ \text{Experimental Probability} = \frac{\text{Number of Heads}}{\text{Total Number of Flips}} = \frac{110}{200} \][/tex]
Simplifying this fraction:
[tex]\[ \text{Experimental Probability} = \frac{11}{20} \][/tex]
### Step 3: Understanding the Theoretical Probability
For a fair coin, the theoretical probability of landing heads up in any single flip is:
[tex]\[ \text{Theoretical Probability} = \frac{1}{2} \][/tex]
### Step 4: Analyzing the Statements
- Statement 1:
"The experimental probability of the coin landing heads up is [tex]\(\frac{1}{2}\)[/tex] and the theoretical probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex]."
This statement is incorrect because the theoretical probability for a fair coin landing heads up should be [tex]\(\frac{1}{2}\)[/tex], not [tex]\(\frac{11}{20}\)[/tex].
- Statement 2:
"The experimental probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex] and the theoretical probability of the coin landing heads up is [tex]\(\frac{1}{2}\)[/tex]."
This statement is correct. The experimental probability, derived from the experiment, is [tex]\(\frac{11}{20}\)[/tex], while the theoretical probability for a fair coin is [tex]\(\frac{1}{2}\)[/tex].
- Statement 3:
"The experimental probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex] and the theoretical probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex]."
This statement is incorrect because the theoretical probability for a fair coin should be [tex]\(\frac{1}{2}\)[/tex], not [tex]\(\frac{11}{20}\)[/tex].
- Statement 4:
"The experimental probability of the coin landing heads up is [tex]\(\frac{1}{2}\)[/tex] and the theoretical probability of the coin landing heads."
This statement is incorrect because the experimental probability calculated from the experiment is [tex]\(\frac{11}{20}\)[/tex].
### Conclusion
The correct statement is:
"The experimental probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex] and the theoretical probability of the coin landing heads up is [tex]\(\frac{1}{2}\)[/tex]."
### Step 1: Understanding the Experiment
Mai flipped a fair coin 200 times, and it landed heads up 110 times.
### Step 2: Calculating the Experimental Probability
The experimental probability is given by the number of times the event occurred divided by the total number of trials. In this case:
[tex]\[ \text{Experimental Probability} = \frac{\text{Number of Heads}}{\text{Total Number of Flips}} = \frac{110}{200} \][/tex]
Simplifying this fraction:
[tex]\[ \text{Experimental Probability} = \frac{11}{20} \][/tex]
### Step 3: Understanding the Theoretical Probability
For a fair coin, the theoretical probability of landing heads up in any single flip is:
[tex]\[ \text{Theoretical Probability} = \frac{1}{2} \][/tex]
### Step 4: Analyzing the Statements
- Statement 1:
"The experimental probability of the coin landing heads up is [tex]\(\frac{1}{2}\)[/tex] and the theoretical probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex]."
This statement is incorrect because the theoretical probability for a fair coin landing heads up should be [tex]\(\frac{1}{2}\)[/tex], not [tex]\(\frac{11}{20}\)[/tex].
- Statement 2:
"The experimental probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex] and the theoretical probability of the coin landing heads up is [tex]\(\frac{1}{2}\)[/tex]."
This statement is correct. The experimental probability, derived from the experiment, is [tex]\(\frac{11}{20}\)[/tex], while the theoretical probability for a fair coin is [tex]\(\frac{1}{2}\)[/tex].
- Statement 3:
"The experimental probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex] and the theoretical probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex]."
This statement is incorrect because the theoretical probability for a fair coin should be [tex]\(\frac{1}{2}\)[/tex], not [tex]\(\frac{11}{20}\)[/tex].
- Statement 4:
"The experimental probability of the coin landing heads up is [tex]\(\frac{1}{2}\)[/tex] and the theoretical probability of the coin landing heads."
This statement is incorrect because the experimental probability calculated from the experiment is [tex]\(\frac{11}{20}\)[/tex].
### Conclusion
The correct statement is:
"The experimental probability of the coin landing heads up is [tex]\(\frac{11}{20}\)[/tex] and the theoretical probability of the coin landing heads up is [tex]\(\frac{1}{2}\)[/tex]."
