To differentiate between experimental and theoretical probability in the context of this question, we can first define each:
- Experimental Probability is determined by conducting an experiment and observing the outcomes. In this case, Pashmina flipped a double-sided coin 20 times and observed that it landed on heads 15 times. Therefore, the experimental probability \( P(E) \) of landing on heads is calculated as:
\[ P(E) = \frac{\text{Number of heads}}{\text{Total flips}} = \frac{15}{20} = \frac{3}{4}. \]
- Theoretical Probability is based on expected outcomes when all outcomes are equally likely, without performing any actual experiments. For a fair double-sided coin, the theoretical probability \( P(T) \) of landing on heads is:
\[ P(T) = \frac{\text{Number of favorable outcomes (heads)}}{\text{Total outcomes (heads or tails)}} = \frac{1}{2}. \]
Now let's summarize the answer to the specific question:
The theoretical probability that a fair double-sided coin will land on heads is \( \frac{1}{2} \).
In the provided options, none of them mention \( \frac{1}{2} \) as an answer. It seems you may be looking for the experimental probability based on the 20 flips, which would be \( \frac{3}{4} \) (or 75%). Thus, for this context:
- The experimental probability is \( \frac{3}{4} \).
- The theoretical probability is \( \frac{1}{2} \).
Since the direct answer to your question about the theoretical probability is not in the choices given, please clarify if you need a specific response based on the experimental data provided, or if there's anything else you'd like to explore.