To answer your questions, we'll first analyze the spinner outcomes and then discuss the coin flip probabilities.
Spinner Outcomes:
The theoretical probability for each section (A, B, and C) of the spinner is as follows:
- A: \( \frac{1}{3} \)
- B: \( \frac{1}{3} \)
- C: \( \frac{1}{3} \)
Now let's calculate the experimental probabilities based on the results from the spins:
- Experimental Probability of A: \( \frac{28}{60} = \frac{14}{30} \approx 0.467 \)
- Experimental Probability of B: \( \frac{15}{60} = \frac{1}{4} = 0.25 \)
- Experimental Probability of C: \( \frac{17}{60} \approx 0.283 \)
Now, let's compare these to the theoretical probabilities:
-
Theoretical Probability for A: \( \frac{1}{3} \approx 0.333 \)
- Comparison: The experimental probability for A (0.467) is greater than the theoretical probability.
-
Theoretical Probability for B: \( \frac{1}{3} \approx 0.333 \)
- Comparison: The experimental probability for B (0.25) is less than the theoretical probability, not greater.
-
Theoretical Probability for C: \( \frac{1}{3} \approx 0.333 \)
- Comparison: The experimental probability for C (0.283) is less than the theoretical probability, not greater.
Conclusion for Spinner:
The experimental probability for A is greater than the theoretical probability. Therefore, the correct answer is:
- The experimental probability for A is greater than the theoretical probability.
Coin Flip Outcomes:
When a fair coin is flipped twice, the possible outcomes are:
- HH (Heads, Heads)
- HT (Heads, Tails)
- TH (Tails, Heads)
- TT (Tails, Tails)
The total number of outcomes is 4. We want to find the probability of getting at least one heads. The favorable outcomes for at least one heads are HH, HT, and TH, which gives us 3 favorable outcomes.
The probability of getting at least one heads is:
\[ P(\text{at least one heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{4} \]
Conclusion for Coin Flips:
The probability of getting at least one heads is:
- 3/4