Question
Peter tossed a fair coin 75 times. The heads appeared 30 times. Which of the following statements is true in the probability of heads?
Experimental probability is more than the theoretical probability in the probability of heads.
Experimental probability is less than the theoretical probability in the probability of heads.
Experimental probability is same as the theoretical probability in the probability of heads.
Experimental probability is two times more than the theoretical probability in the probability of heads.
Experimental probability is more than the theoretical probability in the probability of heads.
Experimental probability is less than the theoretical probability in the probability of heads.
Experimental probability is same as the theoretical probability in the probability of heads.
Experimental probability is two times more than the theoretical probability in the probability of heads.
Answers
Answered by
GPT-4o mini
To determine the relationship between the experimental probability and the theoretical probability of heads from Peter's coin tosses, we need to calculate both probabilities.
1. **Theoretical Probability (TP)**: For a fair coin, the theoretical probability of getting heads is:
\[
\text{TP} = \frac{1}{2} = 0.5
\]
2. **Experimental Probability (EP)**: The experimental probability is calculated based on the results of the experiment. Peter tossed the coin 75 times and got heads 30 times, so the experimental probability of heads is:
\[
\text{EP} = \frac{\text{Number of heads}}{\text{Total tosses}} = \frac{30}{75} = 0.4
\]
Now we can compare the two probabilities:
- Theoretical Probability: 0.5
- Experimental Probability: 0.4
Based on this comparison:
- The experimental probability (0.4) is less than the theoretical probability (0.5).
Thus, the correct statement is:
**Experimental probability is less than the theoretical probability in the probability of heads.**
1. **Theoretical Probability (TP)**: For a fair coin, the theoretical probability of getting heads is:
\[
\text{TP} = \frac{1}{2} = 0.5
\]
2. **Experimental Probability (EP)**: The experimental probability is calculated based on the results of the experiment. Peter tossed the coin 75 times and got heads 30 times, so the experimental probability of heads is:
\[
\text{EP} = \frac{\text{Number of heads}}{\text{Total tosses}} = \frac{30}{75} = 0.4
\]
Now we can compare the two probabilities:
- Theoretical Probability: 0.5
- Experimental Probability: 0.4
Based on this comparison:
- The experimental probability (0.4) is less than the theoretical probability (0.5).
Thus, the correct statement is:
**Experimental probability is less than the theoretical probability in the probability of heads.**