Question
Sadiq rolls a regular six-sided number cube 10 times and gets an even number 7 times. How does his experimental probability compare to the theoretical probability?(1 point)
Responses
The theoretical probability is greater than the experimental probability.
The theoretical probability is greater than the experimental probability.
The theoretical and experimental probabilities are opposites.
The theoretical and experimental probabilities are opposites.
The experimental probability was greater than the theoretical probability.
The experimental probability was greater than the theoretical probability.
The experimental and theoretical probability are equal.
The experimental and theoretical probability are equal.
Responses
The theoretical probability is greater than the experimental probability.
The theoretical probability is greater than the experimental probability.
The theoretical and experimental probabilities are opposites.
The theoretical and experimental probabilities are opposites.
The experimental probability was greater than the theoretical probability.
The experimental probability was greater than the theoretical probability.
The experimental and theoretical probability are equal.
The experimental and theoretical probability are equal.
Answers
GPT-4o mini
To compare Sadiq's experimental probability to the theoretical probability, we should first determine both probabilities.
**Theoretical Probability:**
A regular six-sided number cube (die) has the numbers 1, 2, 3, 4, 5, and 6. The even numbers on the die are 2, 4, and 6. There are 3 even numbers out of a total of 6 numbers.
The theoretical probability of rolling an even number is:
\[
P(\text{Even}) = \frac{\text{Number of Even Outcomes}}{\text{Total Outcomes}} = \frac{3}{6} = \frac{1}{2} = 0.5
\]
**Experimental Probability:**
Sadiq rolled the die 10 times and got an even number 7 times. Therefore, the experimental probability of rolling an even number is:
\[
P(\text{Even, Experimental}) = \frac{\text{Number of Even Outcomes}}{\text{Total Rolls}} = \frac{7}{10} = 0.7
\]
**Comparison:**
- The theoretical probability of rolling an even number is 0.5.
- The experimental probability of rolling an even number, based on Sadiq's rolls, is 0.7.
Hence, since 0.7 (experimental) is greater than 0.5 (theoretical), we conclude that:
**The experimental probability was greater than the theoretical probability.**
**Theoretical Probability:**
A regular six-sided number cube (die) has the numbers 1, 2, 3, 4, 5, and 6. The even numbers on the die are 2, 4, and 6. There are 3 even numbers out of a total of 6 numbers.
The theoretical probability of rolling an even number is:
\[
P(\text{Even}) = \frac{\text{Number of Even Outcomes}}{\text{Total Outcomes}} = \frac{3}{6} = \frac{1}{2} = 0.5
\]
**Experimental Probability:**
Sadiq rolled the die 10 times and got an even number 7 times. Therefore, the experimental probability of rolling an even number is:
\[
P(\text{Even, Experimental}) = \frac{\text{Number of Even Outcomes}}{\text{Total Rolls}} = \frac{7}{10} = 0.7
\]
**Comparison:**
- The theoretical probability of rolling an even number is 0.5.
- The experimental probability of rolling an even number, based on Sadiq's rolls, is 0.7.
Hence, since 0.7 (experimental) is greater than 0.5 (theoretical), we conclude that:
**The experimental probability was greater than the theoretical probability.**