To differentiate between experimental and theoretical probability in the context of Pashmina flipping a double-sided coin, let's define both concepts:
-
Theoretical Probability: This is what you expect to happen in a perfectly controlled scenario based on known principles. For a fair double-sided coin, the theoretical probability of getting heads (P(heads)) is calculated as follows:
\[ P(\text{heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{2} \]
So, the theoretical probability of landing on heads is \( \frac{1}{2} \).
-
Experimental Probability: This is based on actual experiments or observations. In Pashmina's case, she flipped the coin 20 times and got heads 15 times. The experimental probability (P_exp) of getting heads based on her experiment would be calculated as:
\[ P_{\text{exp}}(\text{heads}) = \frac{\text{Number of heads observed}}{\text{Total number of flips}} = \frac{15}{20} = \frac{3}{4} \]
So, to directly answer your question: the theoretical probability of the coin landing on heads is \( \frac{1}{2} \).
From the options you provided:
- \( \frac{1}{2} \) is the theoretical probability.
- \( \frac{3}{4} \) is the experimental probability derived from her flips.
Thus, the theoretical probability that it will land on heads is \( \frac{1}{2} \).