Differentiate between experimental and theoretical probability in the following question. Pashmina flips a double-sided coin 20 times, and it lands on heads 15 times. What is the theoretical probability that it will land on heads?(1 point)

Responses

14
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34
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25

1 answer

To differentiate between experimental and theoretical probability in your question:

  • Theoretical Probability is based on the assumption of a fair situation where all outcomes are equally likely. For a double-sided coin, the probability of landing on heads (assuming it's a fair coin) is calculated as follows:

    \[ \text{Theoretical Probability of Heads} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{2} \]

So, the theoretical probability of getting heads when flipping a double-sided coin is \( \frac{1}{2} \) or 50%.

  • Experimental Probability, on the other hand, is based on the actual results of an experiment. In this case, Pashmina flipped the coin 20 times and observed that it landed on heads 15 times. Therefore, the experimental probability of getting heads is calculated as:

    \[ \text{Experimental Probability of Heads} = \frac{\text{Number of heads obtained}}{\text{Total flips}} = \frac{15}{20} = \frac{3}{4} \]

In summary:

  • Theoretical Probability of heads = \( \frac{1}{2} \)
  • Experimental Probability of heads = \( \frac{3}{4} \)

Regarding your question, the answer for the theoretical probability that the coin will land on heads is \( \frac{1}{2} \).

From the options you provided, none state \( \frac{1}{2} \), but that is the correct answer for the theoretical probability.