Brandon flips two fair coins multiple times and records the frequency of the results in the following table.
50 trials|125trials|150trials
HH 10 33 37
TH 9 31 38
HT 13 28 38
TT 18 33 37
DETERMINE THE EXPERIMENTAL PROBABILITY AND THEORETICAL PROBABILITY FOR EACH OUTCOME IN EACH SET OF BRANDON'S TRIALS. HOW DO THE EXPERIMANTAL PRBABILITY AND THEORECTICAL PROBABILITY RELATE TO EACH OTHER FOR EACH OF THE 3 SETS OF TRIALS?
Explain your answer, providing calculations or any other strategy that will support your reasoning.
I’m stuck on this aswell lmao
To determine the experimental probability and theoretical probability for each outcome in each set of Brandon's trials, we need to calculate the number of times each outcome occurred and divide it by the total number of trials.
Let's start with the first set of trials, consisting of 50 trials:
Experimental Probability:
- For the outcome HH: 10 occurrences / 50 trials = 0.2
- For the outcome TH: 9 occurrences / 50 trials = 0.18
- For the outcome HT: 13 occurrences / 50 trials = 0.26
- For the outcome TT: 18 occurrences / 50 trials = 0.36
Now let's calculate the theoretical probability. Since Brandon is flipping two fair coins, there are four possible outcomes (HH, TH, HT, and TT), and each outcome has a 1/4 or 0.25 chance of occurring.
Theoretical Probability:
- For HH: 0.25
- For TH: 0.25
- For HT: 0.25
- For TT: 0.25
For the second set of trials consisting of 125 trials, we repeat the same calculations:
Experimental Probability:
- HH: 33 occurrences / 125 trials = 0.264
- TH: 31 occurrences / 125 trials = 0.248
- HT: 28 occurrences / 125 trials = 0.224
- TT: 33 occurrences / 125 trials = 0.264
Theoretical Probability:
- HH: 0.25
- TH: 0.25
- HT: 0.25
- TT: 0.25
Finally, for the third set of trials consisting of 150 trials:
Experimental Probability:
- HH: 37 occurrences / 150 trials = 0.2467
- TH: 38 occurrences / 150 trials = 0.2533
- HT: 38 occurrences / 150 trials = 0.2533
- TT: 37 occurrences / 150 trials = 0.2467
Theoretical Probability:
- HH: 0.25
- TH: 0.25
- HT: 0.25
- TT: 0.25
Now, let's analyze the relationship between experimental probability and theoretical probability for each set of trials.
In ideal conditions, the experimental probability should converge to the theoretical probability as the number of trials increase. However, due to the random nature of coin flips, there is bound to be some variation between the experimental and theoretical probabilities.
Looking at the three sets of trials, we can observe that as the number of trials increases, the experimental probabilities tend to get closer to the theoretical probabilities. However, there is still some deviation due to chance. In general, the larger the number of trials, the smaller the difference between the experimental and theoretical probabilities. This is known as the Law of Large Numbers, which suggests that with more trials, the experimental results will approach the theoretical probabilities more closely.
In summary, while the experimental probabilities are not an exact match to the theoretical probabilities in each set of trials, they tend to get closer as the number of trials increases.