a) List the sample space for flipping a coin.
b) Assign theoretical probabilities for each outcome.
c) Using theoretical probabilities, predict the relative frequency for each outcome given 20 trials
a) The sample space for flipping a coin is {heads, tails}.
b) The theoretical probability of getting heads is 0.5 or 50%, while the theoretical probability of getting tails is also 0.5 or 50%.
c) Predicting the relative frequency for each outcome using theoretical probabilities, we can expect to get heads approximately 10 times (50% of 20) and tails approximately 10 times (50% of 20) in 20 trials of flipping a coin. However, this is only a prediction and the actual outcome may vary.
What is a fraction theoretical probability when flipping a coin
The theoretical probability of flipping a coin is a fraction because it is the ratio of the number of desired outcomes to the total number of possible outcomes. In the case of flipping a coin, there are two possible outcomes (heads or tails), and the fraction theoretical probability of getting heads is 1/2 or 0.5, and the fraction theoretical probability of getting tails is also 1/2 or 0.5.
Outcomes Tally Frequency
Heads IIIII/III 13
Tails IIIII/II 7
Total IIIII/IIIII/IIIII/IIIII 20
c) Calculate the relative frequencies for flipping a coin based on your results from tasks a) and b).
Without technology (a)
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Task 2
a) Conduct repeated single-step chance experiments without technology, flipping the coin 20 times and recording the results in the frequency table below.
Table 1. Results of Trial 1 – Without technology
Outcomes Tally Frequency
Heads IIIII/III 8
Tails IIIII/IIIII/II 12
Total IIIII/IIIII/IIIII/IIIII 20
b)
Outcomes Tally Frequency
Heads IIIII/III 13
Tails IIIII/II 7
Total IIIII/IIIII/IIIII/IIIII 20
c) Calculate the relative frequencies for flipping a coin based on your results from tasks a) and b).
Without technology (a)
With technology (b)
For Task 2a:
The relative frequency for getting Heads is 8/20 = 0.4 or 40%.
The relative frequency for getting Tails is 12/20 = 0.6 or 60%.
For Task 2b:
The relative frequency for getting Heads is 13/20 = 0.65 or 65%.
The relative frequency for getting Tails is 7/20 = 0.35 or 35%.
Note: The relative frequency is calculated by dividing the frequency of a specific outcome by the total number of trials (in this case, 20).