Ignite
Rug Games Lesson
Probability
Each diagram in this activity represents a rug. Imagine that a trap door opens directly over the rug. A dart falls through the door, landing at random somewhere on the rug. In other words, every point on the rug has the same chance of getting hit as every other point.
If you were trying to predict which part of the rug will get hit. Each color is worth a different amount of points. Which color would you choose, gray or white?
If you were trying to predict which part of the rug will get hit. Each color is worth a different amount of points. Which color would you choose, gray or white?
To find the probability of white spaces and gray spaces you first have to find the smallest shape and cut the rug into the same size.
Expected Value |
When you cut the rug into equal pieces you count how many shapes in total are in the rug. Then you write half of a fractions with the number of shapes on the bottom next to the colors in the rug. Then count how many shapes in a certain color are in the rug, then write the number in the fraction with the color it was from. Do with both colors and then you have the probability the dart hitting different colors on the rug.
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Now that we know the probability of a dart hitting a gray area and white area we have to calculate the Expected Value to see which color is better to pick. You get the expected value by mulitplying the probability by the number of points the area is worth. For Gray, that would be 8/15*6=48/15. Next you do the same with the white probability. 7/15*8=56/15.
This means that White has a lower probability of getting hit by the dart but has a higher expected value. This is very similar to the lottery. There is all low probability that you will win but the expected value is so high that makes people want to participate. |
I learned about theretical probability and experimental probability as well. Theretical Probability is based on theory. You already know exactly how many possible outcomes there are and you know how many times a certain outcome will happen. For example rolling a die you know that there are six possible numbers you can get, and you can get each number only once.
Experimental Probability is based on experiments. You try to collect data and put it together to try to make a prediction as accurate as possible. An example is predicting whether or not it rains. It is not always right but it is based off past data and is analyzed to make the most accurate prediction. These two different types of probability are about doing the same thing, but the numbers are different.
The reason probability is important is that it helps predict things that can happen in real life such as the probability of getting a head when flipping a coin. It can help us make better choices when it comes to Health care and can help with playing board games and you're trying to roll a double. Probability is connect with all sorts of things in the real world. When I learned about this it helped me connect to a lot of activities that I know of that have to do with trying to predict outcomes and it gave me a new perspective. This skill can help me find out if which choices are best for me and help me become more proficient in math.
Experimental Probability is based on experiments. You try to collect data and put it together to try to make a prediction as accurate as possible. An example is predicting whether or not it rains. It is not always right but it is based off past data and is analyzed to make the most accurate prediction. These two different types of probability are about doing the same thing, but the numbers are different.
The reason probability is important is that it helps predict things that can happen in real life such as the probability of getting a head when flipping a coin. It can help us make better choices when it comes to Health care and can help with playing board games and you're trying to roll a double. Probability is connect with all sorts of things in the real world. When I learned about this it helped me connect to a lot of activities that I know of that have to do with trying to predict outcomes and it gave me a new perspective. This skill can help me find out if which choices are best for me and help me become more proficient in math.