https://file.aiquickdraw.com/mathbot/file/1727465441914jygm0i0k.jpg

The problem involves determining whether a coin is fair based on a simulation and actual flipping results.

**Analysis:**
1. The histogram shows the results of 200 simulations of flipping a coin 50 times. The x-axis represents the proportion of flips that result in heads, and the y-axis shows the relative frequency of these proportions.
2. The peak of the histogram is around 0.5, which suggests that most of the simulations resulted in close to half heads, supporting the claim that the coin is fair.
3. You flipped the actual coin 50 times and got 26 heads. This results in a proportion of \( \frac{26}{50} = 0.52 \).

**Conclusion:**
The observed proportion of 0.52 falls near the peak of the histogram, indicating that getting 26 heads in 50 flips is consistent with what we would expect from a fair coin. 

**Answer:**
"The maker's claim is most likely true."

Would you like a detailed explanation or have any questions? Here are some related questions to consider:

1. What is the probability of getting exactly 25 heads in 50 coin flips?
2. How do you calculate the expected proportion of heads in a large number of coin flips?
3. What is the standard deviation for the number of heads in 50 coin flips?
4. How would the conclusion change if 40 heads were observed instead of 26?
5. How can simulations be used to assess fairness in other probabilistic scenarios?

**Tip:** When evaluating fairness using simulations, always compare observed results to the range of expected outcomes, not just the mean.

You flip a coin 5 times and do not get a tails. You suspect this coin favors heads. The coin maker claims that the coin does not favor heads or tails. You use technology to simulate 200 random samples of flipping a coin 50 times. The histogram shows the results. What should you conclude when you flip the actual coin 50 times and get 26 heads?

Analyze the fairness of a coin using simulation and probability. With 200 random samples of flipping a coin 50 times, this problem involves concepts like expected proportion, the binomial distribution, and statistical simulation. This is ideal for Grades 9-12 students learning about probability and statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation