Outcomes Experimental Theoretical Are the experimental and theoretical frequencies the same?
Heads With technology: 8/30
Without technology: 13/30 1/2 No, they are not the same. But However, Without technology is the closest out of them with 13/30 flipped heads. And with technology Flipped 8/30 times.
Tails With technology:12/30
Without technology: 7/30 1/2 No, they are not the same. But However, With technology is the closest out of them with 12/30 flipped tail and with technology got flipped 7/30 times.
Explain the variation between the experimental and theoretical relative frequencies.
The variation between the experimental and theoretical relative frequencies may be due to chance or random variation, as well as other factors such as sample size and sampling method. The experimental frequencies are based on actual observations from a sample, while the theoretical frequencies are based on mathematical or theoretical models. In some cases, the experimental and theoretical frequencies may be very close or even identical, but in other cases, there may be some discrepancy due to these factors. However, as the sample size increases and the sampling method becomes more random, the experimental frequencies should become closer to the theoretical frequencies.
Task 3. Extension exercise
a) Add an extra coin.
b) Identify the sample space for flipping 2 coins by completing the following table.
Heads Tails
Heads HH - HT -
Tails TH - TT -
1,4,
c) Using the table above, determine the theoretical probability of flipping two tails.
a) With an extra coin, we would be flipping 3 coins in total.
b) Sample space for flipping 2 coins:
Heads Tails
Heads HH - HT -
Tails TH - TT -
The four possible outcomes are: HH, HT, TH, and TT.
c) The theoretical probability of flipping two tails is 1/4 or 0.25 since there is only one way to get two tails (TT) out of the four possible outcomes.
d) Predict the probability of achieving two tails if the coins are flipped 10 times.
If we flip two coins 10 times, the probability of flipping two tails in each of those independent trials would be 1/4 or 0.25. The probability of getting two tails at least once in 10 trials can be calculated using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
The probability of not getting two tails in a single trial is 3/4 (1 - 1/4). Therefore, the probability of not getting two tails in all ten trials is (3/4)^10, or approximately 0.056.
Using the complement rule, the probability of getting at least one pair of tails in 10 trials is 1 - 0.056, or approximately 0.944 or 94.4%. So there is a very high chance of achieving two tails at least once in 10 coin flips.
The variation between the experimental and theoretical relative frequencies can be explained by the presence of random chance and potential deviations from the expected outcomes.
Theoretical frequencies are calculated based on mathematical models or statistical principles that represent the expected probabilities of different outcomes. These probabilities are derived from assumptions or established theories.
On the other hand, experimental frequencies are obtained through actual observations or measurements in a real-world situation. In this case, the frequencies of flipping heads and tails were observed with and without technology.
The variation between the experimental and theoretical frequencies can occur due to various factors. One such factor is random chance. When conducting experiments, there is always a level of uncertainty associated with individual outcomes. Even if the theoretical probabilities are accurate, the actual observations may deviate from these expected values due to random variation.
Another factor that can contribute to the variation is the presence of other influencing factors that are not accounted for in the theoretical model. In this case, the presence or absence of technology may affect the outcome of the coin flips, resulting in different frequencies than what would be predicted by the theoretical model.
It is important to note that, while the experimental and theoretical frequencies may not be exactly the same, it does not necessarily mean that the theoretical model is incorrect. The variation between the two can provide valuable insights into the limitations or factors influencing the outcomes in real-world scenarios.
To summarize, the variation between experimental and theoretical frequencies can be attributed to random chance and potential deviations from the expected outcomes due to unaccounted factors. It is important to analyze and compare these variations to gain a better understanding of the underlying processes and to refine or adjust the theoretical models if necessary.