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.

The theoretical probabiliyt for any of the events is 1/2*1/2=1/4

the experimental probability for any trial is the number of successes divided by the trials. Example: TT(50) = 18/50=9/25=.36

Dont forget each outcome is random...

To determine the experimental and theoretical probabilities for each outcome in each set of Brandon's trials, we need to first understand what these terms mean.

Experimental probability is the probability obtained from performing actual experiments or trials and calculating the ratio of favorable outcomes to the total number of trials. This gives us an estimate of the probability based on the observed results.

Theoretical probability, on the other hand, is the probability calculated based on the assumption that all outcomes are equally likely. It is obtained by dividing the number of favorable outcomes by the total number of possible outcomes.

Let's calculate the experimental and theoretical probabilities for each outcome in each set of trials:

For the first set of trials (50 trials):

Experimental probability of HH = Number of HH outcomes / Total number of trials = 10 / 50 = 0.2
Theoretical probability of HH = Number of HH outcomes / Total number of possible outcomes = 10 / 4 = 0.25

Experimental probability of TH = 9 / 50 = 0.18
Theoretical probability of TH = 9 / 4 = 0.225

Experimental probability of HT = 13 / 50 = 0.26
Theoretical probability of HT = 13 / 4 = 0.325

Experimental probability of TT = 18 / 50 = 0.36
Theoretical probability of TT = 18 / 4 = 0.45

For the second set of trials (125 trials):

Experimental probability of HH = 33 / 125 = 0.264
Theoretical probability of HH = 33 / 4 = 0.825

Experimental probability of TH = 31 / 125 = 0.248
Theoretical probability of TH = 31 / 4 = 0.775

Experimental probability of HT = 28 / 125 = 0.224
Theoretical probability of HT = 28 / 4 = 0.7

Experimental probability of TT = 33 / 125 = 0.264
Theoretical probability of TT = 33 / 4 = 0.825

For the third set of trials (150 trials):

Experimental probability of HH = 37 / 150 = 0.247
Theoretical probability of HH = 37 / 4 = 0.925

Experimental probability of TH = 38 / 150 = 0.253
Theoretical probability of TH = 38 / 4 = 0.95

Experimental probability of HT = 38 / 150 = 0.253
Theoretical probability of HT = 38 / 4 = 0.95

Experimental probability of TT = 37 / 150 = 0.247
Theoretical probability of TT = 37 / 4 = 0.925

Now, let's analyze the relationship between experimental and theoretical probabilities for each set of trials:

In general, experimental probabilities are expected to approach theoretical probabilities as the number of trials increases.

For the first set of trials, the experimental and theoretical probabilities are relatively close, but not exact. This discrepancy could be due to the small number of trials.

However, as the number of trials increases in the second and third sets, we can observe that the experimental probabilities are becoming closer to the theoretical probabilities. This demonstrates that the experimental results are converging towards the expected values.

Therefore, we can conclude that the experimental probability and theoretical probability tend to become more similar as the number of trials increases, indicating that the experimental results become more reliable and representative of the theoretical probabilities.