1. How do you find the experimental probability that a particular result will occur? Why is it called the experimental probability?
How: To find experimental probability you need to first perform the experiment at hand. Whether it's tossing coins or cups, flipping spoons, or even spinner a spinner, you have to first perform the experiment. For example, lets say that Mary wants to decide which desert to eat for dinner everyday of June-- either fruit, heads, or ice cream, tails. She does a trail to see what the probable outcome will be, tossing the coin 30 times. She needs to record the number of heads out of 30 and the number of tails out of 30. You would perform this experiment and record the results-- heads: 14 times and tails: 16 times. Secondly, you would right out the fraction/relative frequency using formal probability notation with the certain parameters that were chosen at the beginning of the experiment-- heads: 14/30 and tails: 16/30. Then, you would convert that fraction into a percentage, and after this, you can finally begin analyzing the data and begin making predictions about future outcomes.
Why: The experimental probability, relative frequency, or also known as the empirical probability, is the ratio of the number of outcomes in which a specified event occurs to the total number of trials in an experiment. Lastly, it's called experimental probability because the predictions and the outcomes are based off trials formed from an experiment.
2. In an experiment, are 30 trials as good as 500 trials to predict the chances of a result? Explain.
NO... NEVER! In an experiment 30 trials is not as food as 500 trials to predict the chances of a result. The golden rule is that the more data, trails, and evidence you have, the better. When you are performing an experiment, you have to always try to have somewhat accurate results otherwise this doesn't help you in getting the information needed to solve your question or make further choices and predictions. Again, the more trials you have, the more accurate the results of you experiment will be as you have more and more data to work with. To predict the chances of a certain result through the experiment, you need to base that prediction off of good data that's somewhat reliable and can be almost accurate. A connection to a previous unit is the Are You Normal unit, the math teachers collect a huge sample size of all math students in a survey and then we analyzed the data. To do this experiment in the previous unit we need a big sample as the it was a very large survey and there weren't that many common answers. So to make a prediction on the population we needed a large sample, otherwise the data would be very hard to analyze. This idea of 500 trials being better than 30 trials directly relates to this previous unit.
3. What does it mean for the results to be equally likely?
For results to be equally likely, they all have to have the same chances of occurring. It also means that the experiment has to be unbiased and fair. However, equally likely doesn't mean that results have a 50% and 50% chance. The most important part of determining if something is equally likely to another, you have to now how many parameters were set for the experiment. For example, if you have 4 different parameters or options, you would have to distribute these parameters or 100% evenly among these 4 parameters. Therefore, they would have the same chance of occurring, making none of them less likely to occur than another. Going with the example below each parameter or result would have 25% chance of occurring, and the results would be equally likely.
How: To find experimental probability you need to first perform the experiment at hand. Whether it's tossing coins or cups, flipping spoons, or even spinner a spinner, you have to first perform the experiment. For example, lets say that Mary wants to decide which desert to eat for dinner everyday of June-- either fruit, heads, or ice cream, tails. She does a trail to see what the probable outcome will be, tossing the coin 30 times. She needs to record the number of heads out of 30 and the number of tails out of 30. You would perform this experiment and record the results-- heads: 14 times and tails: 16 times. Secondly, you would right out the fraction/relative frequency using formal probability notation with the certain parameters that were chosen at the beginning of the experiment-- heads: 14/30 and tails: 16/30. Then, you would convert that fraction into a percentage, and after this, you can finally begin analyzing the data and begin making predictions about future outcomes.
Why: The experimental probability, relative frequency, or also known as the empirical probability, is the ratio of the number of outcomes in which a specified event occurs to the total number of trials in an experiment. Lastly, it's called experimental probability because the predictions and the outcomes are based off trials formed from an experiment.
2. In an experiment, are 30 trials as good as 500 trials to predict the chances of a result? Explain.
NO... NEVER! In an experiment 30 trials is not as food as 500 trials to predict the chances of a result. The golden rule is that the more data, trails, and evidence you have, the better. When you are performing an experiment, you have to always try to have somewhat accurate results otherwise this doesn't help you in getting the information needed to solve your question or make further choices and predictions. Again, the more trials you have, the more accurate the results of you experiment will be as you have more and more data to work with. To predict the chances of a certain result through the experiment, you need to base that prediction off of good data that's somewhat reliable and can be almost accurate. A connection to a previous unit is the Are You Normal unit, the math teachers collect a huge sample size of all math students in a survey and then we analyzed the data. To do this experiment in the previous unit we need a big sample as the it was a very large survey and there weren't that many common answers. So to make a prediction on the population we needed a large sample, otherwise the data would be very hard to analyze. This idea of 500 trials being better than 30 trials directly relates to this previous unit.
3. What does it mean for the results to be equally likely?
For results to be equally likely, they all have to have the same chances of occurring. It also means that the experiment has to be unbiased and fair. However, equally likely doesn't mean that results have a 50% and 50% chance. The most important part of determining if something is equally likely to another, you have to now how many parameters were set for the experiment. For example, if you have 4 different parameters or options, you would have to distribute these parameters or 100% evenly among these 4 parameters. Therefore, they would have the same chance of occurring, making none of them less likely to occur than another. Going with the example below each parameter or result would have 25% chance of occurring, and the results would be equally likely.
Anya, great response. Good connection to the "Are You Normal?" unit. The "equally likely" comment about not needing to be 50:50 is also very good.
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