To differentiate between experimental and theoretical probability, let's first define each term:
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Theoretical Probability: This is the probability of an event happening based on all possible outcomes, assuming that all outcomes are equally likely. For example, when flipping a fair coin, the theoretical probability of landing on heads is calculated as follows: \[ P(\text{Heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{2}. \] In the case of a double-sided coin (where both sides are heads), theoretically it will always land on heads, hence: \[ P(\text{Heads}) = 1. \]
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Experimental Probability: This is the probability of an event based on actual experiments or observations. It is calculated by the ratio of the number of times an event occurs to the total number of trials. In your question, after flipping the double-sided coin 20 times, it landed on heads 15 times. The experimental probability can be calculated as: \[ P(\text{Heads}) = \frac{\text{Number of heads observed}}{\text{Total number of flips}} = \frac{15}{20} = 0.75. \]
In summary, for the question provided:
- The theoretical probability of landing on heads with a double-sided coin is 1 (since it will always land on heads).
- The experimental probability based on the 20 flips is 0.75 (since it landed on heads 15 times).
Thus, theoretical probability is based on the expected outcome in an ideal situation, while experimental probability is based on actual results from trials.
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