Question

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

34
Start Fraction 3 over 4 End Fraction

14
Start Fraction 1 over 4 End Fraction

12
Start Fraction 1 over 2 End Fraction

25

Answer 1

In the context of probability, experimental probability refers to the likelihood of an event based on the actual results of an experiment, while theoretical probability is based on the expected outcomes assuming all outcomes are equally likely.

In the case of Pashmina flipping a double-sided coin:

1. **Experimental Probability**: This is determined by actual outcomes from the flips. Pashmina flipped the coin 20 times and got heads 15 times, so the experimental probability of landing on heads is calculated as:
\[
\text{Experimental Probability of Heads} = \frac{\text{Number of Heads}}{\text{Total Flips}} = \frac{15}{20} = \frac{3}{4}
\]

2. **Theoretical Probability**: This is the expected outcome for a fair double-sided coin, where there are two equally likely outcomes (heads or tails). The theoretical probability of landing on heads is:
\[
\text{Theoretical Probability of Heads} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{1}{2}
\]

From the options provided, the answer for the theoretical probability that it will land on heads is:
\[
\frac{1}{2}
\]

Thus the differences can be summarized as follows:
- **Experimental Probability**: \(\frac{3}{4}\) based on the outcomes of the actual flips.
- **Theoretical Probability**: \(\frac{1}{2}\) based on expected outcomes for a fair coin flip.

The correct answer for the theoretical probability in the question is:
\[
\frac{1}{2}
\]