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.
5 answers
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) 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.
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 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.
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