Theoretical probability is based on the expected outcomes in a perfectly controlled scenario, while experimental probability is based on actual results observed during an experiment.
In the case of Pashmina flipping a double-sided coin, the theoretical probability of landing on heads is calculated based on the assumption that the coin is fair. For a fair coin, there are two equally likely outcomes: heads or tails. Therefore, the theoretical probability \( P \) of landing on heads is:
\[ P(\text{heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{2} \]
So, the correct answer from the options given is:
Start Fraction 1 over 2 End Fraction (or \( \frac{1}{2} \))
The experimental probability in this case would be based on Pashmina's results from the 20 flips, which shows that it landed on heads 15 times. The experimental probability, calculated from the results, would be:
\[ P(\text{heads, experimental}) = \frac{15}{20} = \frac{3}{4} \]
In summary:
- Theoretical Probability: \(\frac{1}{2}\)
- Experimental Probability: \(\frac{3}{4}\) based on Pashmina's flips.