Mr. Carter wants to determine the probabilities for students choosing a hamburger or a hot dog at the school picnic.
A. Explain how Mr. Carter could create a simulation for this using a coin.
B. Should Mr. Carter flip the coin 5 times or 50 times to get the best results in this simulation? Explain your answer.
A. To create a simulation using a coin, Mr. Carter can assign "heads" to represent choosing a hamburger and "tails" to represent choosing a hot dog. He can then flip the coin multiple times and observe the outcome to approximate the probabilities.
Here's an explanation of the process:
1. Assign "heads" to represent a hamburger and "tails" to represent a hot dog. Set the coin on a flat surface.
2. Flip the coin once and note the outcome (heads or tails). This represents the choice of one student.
3. Repeat the flip multiple times (e.g., 10, 20, or more) and record the outcomes.
4. Count the number of times the coin landed on "heads" and "tails" separately.
5. Divide the number of times the coin landed on "heads" by the total number of flips to get the probability of choosing a hamburger.
6. Similarly, divide the number of times the coin landed on "tails" by the total number of flips to get the probability of choosing a hot dog.
B. To obtain more accurate results in the simulation, Mr. Carter should flip the coin 50 times rather than just 5 times. This is because with more coin flips, the simulation provides a larger sample size, leading to more reliable estimates of the probabilities.
With only 5 coin flips, the results may easily be skewed due to chance and may not accurately represent the true probabilities of students choosing a hamburger or a hot dog. However, by increasing the number of coin flips to 50, Mr. Carter can reduce the impact of randomness and obtain a more accurate approximation of the probabilities based on a larger sample size.
each flip has a 1/2 chance for each item.
The more trials, the better chance of getting the theoretical expectation.
read up on Monte Carlo methods