Hello,
In a class of 24 students, every student flips fairly two coins 40 times each and records the results. Assume that the class obtained the expected results when they conducted the experiment.
a. Make a bar graph illustrating the combined class results
b. explain why an individual student's results might be different from the class results
a) There are only three possible results of flipping two coins: 2 heads, 2 tails, or one of each.
You have a choice of either faking the results using probabililty theory, or doing the experiment yourself by flipping 40 x 2 x 24 times, but that would take a while. I would do the forty two-coin flipping at least ten times and see what the trends are.
The most likely result is 20 with one of each, 10 with 2 heads, and 10 with 2 tails. But other results are also possible, just less likely
b) There is no reason that one student's results would equal the 24-student class average.
To make a bar graph illustrating the combined class results, you need to count and represent the number of times each possible outcome occurred for all the students in the class.
a. Follow these steps to create the bar graph:
1. Determine the possible outcomes when flipping two coins. There are four possible outcomes: Head-Head (HH), Head-Tail (HT), Tail-Head (TH), and Tail-Tail (TT).
2. Calculate the total number of times each outcome occurred for the entire class. Multiply the number of students (24) by the number of times each student flipped the coins (40). This will give you the total number of flips for the class, which is 24 x 40 = 960.
3. Count the occurrences of each outcome among all the flips. For example, if HH occurred 200 times, HT occurred 300 times, TH occurred 250 times, and TT occurred 210 times, you would have a total of 960 flips.
4. Create a bar graph with the possible outcomes (HH, HT, TH, TT) on the horizontal axis and the number of occurrences on the vertical axis. Each bar will represent the number of times each outcome occurred.
b. An individual student's results might differ from the class results due to inherent randomness in the process of flipping coins. Here are a few reasons why individual results can vary:
1. Sampling variability: Each student only flips the coins 40 times. With a small sample size, it is possible for individual results to deviate from the expected results on a larger scale.
2. Randomness: Flipping coins is a random process, and the outcomes depend on chance. Even though the expected probability of getting heads or tails is 50%, individual results can differ due to random variations.
3. Individual biases: Each student's flipping technique may differ slightly, resulting in different outcomes. Factors such as the force of the flip, the angle at which the coins are flipped, or even minor variations in the coins themselves can influence the results.
Overall, individual students' results may deviate from the class results due to the inherent randomness of coin flips, small sample sizes, and individual biases.