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
25
Start Fraction 2 over 5 End Fraction
34
Start Fraction 3 over 4 End Fraction
14
Start Fraction 1 over 4 End Fraction
12
Start Fraction 1 over 2 End Fraction
Responses
25
Start Fraction 2 over 5 End Fraction
34
Start Fraction 3 over 4 End Fraction
14
Start Fraction 1 over 4 End Fraction
12
Start Fraction 1 over 2 End Fraction
Answers
GPT-4o mini
Theoretical probability is based on the idea of what should happen in an ideal situation, while experimental probability is based on the actual results from an experiment.
In the case of Pashmina flipping a double-sided coin:
1. **Theoretical Probability**: For a fair double-sided coin, each side (heads or tails) has an equal probability of landing face up. Therefore, the theoretical probability of landing on heads is:
\[
P(\text{heads}) = \frac{\text{Number of favorable outcomes (heads)}}{\text{Total possible outcomes (heads + tails)}} = \frac{1}{2}
\]
2. **Experimental Probability**: In Pashmina's experiment, she flipped the coin 20 times and it landed on heads 15 times. The experimental probability of landing on heads in her experiment is:
\[
P(\text{heads, experimental}) = \frac{\text{Number of heads obtained}}{\text{Total flips}} = \frac{15}{20} = \frac{3}{4}
\]
To answer the question, the theoretical probability that the coin will land on heads is:
\[
\frac{1}{2} \text{ (or 12, as represented in your answer choices)}
\]
Thus, the correct response is **12 (Start Fraction 1 over 2 End Fraction)**.
In the case of Pashmina flipping a double-sided coin:
1. **Theoretical Probability**: For a fair double-sided coin, each side (heads or tails) has an equal probability of landing face up. Therefore, the theoretical probability of landing on heads is:
\[
P(\text{heads}) = \frac{\text{Number of favorable outcomes (heads)}}{\text{Total possible outcomes (heads + tails)}} = \frac{1}{2}
\]
2. **Experimental Probability**: In Pashmina's experiment, she flipped the coin 20 times and it landed on heads 15 times. The experimental probability of landing on heads in her experiment is:
\[
P(\text{heads, experimental}) = \frac{\text{Number of heads obtained}}{\text{Total flips}} = \frac{15}{20} = \frac{3}{4}
\]
To answer the question, the theoretical probability that the coin will land on heads is:
\[
\frac{1}{2} \text{ (or 12, as represented in your answer choices)}
\]
Thus, the correct response is **12 (Start Fraction 1 over 2 End Fraction)**.