Question

Explain the variation between the experimental and theoretical relative frequencies.

Answer 1

The experimental relative frequency is the proportion of times an event or outcome occurs in a repeated experiment, while the theoretical relative frequency is the expected proportion of times the same event or outcome should occur based on probability theory. The variation between the experimental and theoretical relative frequencies arises due to sampling variability, measurement errors, and other factors that affect the actual outcomes in the experiment. In some cases, the experimental relative frequency may be close to the theoretical relative frequency if the sample size is large and the experiment is designed correctly. However, in many cases, there may be significant deviations from the theoretical predictions due to random factors and other sources of error. The variation between the experimental and theoretical relative frequencies can be analyzed and quantified using statistical methods such as hypothesis testing, confidence intervals, and regression analysis.

Answer 2

Conduct the experiment flipping two coins 10 times and record the results in the frequency table below. Outcomes are sample spaces identified in task (b).

Outcomes Tally Frequency
HH IIIII/II 7
TT IIIII/ 5
HT II 2
TH IIIII/I 6
Total 20 20

Calculate the relative frequency for each outcome based on your results from task (e).

The relative frequency to HH is 7/20 The relative frequency of HT is 2/20 and the frequency for TH is 6/20 But TT had 5/20 witch is the theoretical frequency of HH,TH,HT,TT.









Compare the theoretical probability with the experimental relative frequency for flipping two tails. Are they the same?

Answer 3

No, they are not the same. The theoretical probability of flipping two tails in two coin flips is 1/4 or 0.25, which means that in a large number of trials, we would expect two tails to occur 25% of the time. However, in this particular experiment where the coins were flipped only 10 times, the experimental relative frequency of flipping two tails is 5/20 or 0.25, which means that two tails were obtained in 25% of the trials. Therefore, in this case, the experimental relative frequency is equal to the theoretical probability for flipping two tails.

Answer 4

Conduct the experiment flipping two coins 20 times and record the results in the frequency table below. Outcomes are sample spaces identified in task (b).

Outcomes Tally Frequency
HH IIIII/II 7
TT IIIII/ 5
HT II 2
TH IIIII/I 6
Total 20 20

Calculate the relative frequency for each outcome based on your results from task (e).

The relative frequency to HH is 7/20 The relative frequency of HT is 2/20 and the frequency for TH is 6/20 But TT had 5/20 witch is the theoretical frequency of HH,TH,HT,TT.









Compare the theoretical probability with the experimental relative frequency for flipping two tails. Are they the same?

Answer 5

No, they are not the same. The theoretical probability of flipping two tails in two coin flips is 1/4 or 0.25, which means that in a large number of trials, we would expect two tails to occur 25% of the time. However, in this particular experiment where the coins were flipped 20 times, the experimental relative frequency of flipping two tails is not provided in the table.