Sure, let's walk through the steps required to verify Elijah's prediction and understand why it is exact.
1. Total Number of Spins:
Elijah is going to spin a spinner a total of 180 times.
2. Prediction:
Elijah predicts that 60 of those 180 spins will land on the section labeled 3.
3. Theoretical Probability:
Assuming the spinner has an equal probability of landing on each section (and likely there are 3 equally-sized sections), the theoretical probability of landing on any specific section, including the section labeled 3, is 1/3.
4. Calculate Theoretical Prediction:
To find the theoretical number of spins that should land on section 3, based on the probability, we multiply the total number of spins by the theoretical probability:
[tex]\[
\text{Theoretical Number of Spins} = 180 \times \frac{1}{3} = 60
\][/tex]
5. Comparison with Elijah’s Prediction:
The value obtained from the theoretical calculation is 60, which matches exactly with Elijah’s prediction of 60 spins landing on the section labeled 3.
6. Conclusion:
Elijah's prediction is precise because he predicted 60 out of 180 spins would land on section labeled 3. Mathematically, this is exactly what the theoretical model predicts since:
[tex]\[
180 \div 3 = 60
\][/tex]
Thus, based on the theoretical probability, Elijah’s prediction is exact.
So, the statement that best describes Elijah's prediction is that it is exact because the theoretical calculations confirm that 60 out of 180 spins will indeed land on the section labeled 3.
