841 Math Blog

In class today we did 3 things. The three things we did were the game titled "Is This Game Fair?", a probability tree, and the race game. Well the race thing was for homework, but everyone should've done that by now. Anyways, I will explain those three things now.


1. Is This Game Fair?
In class, we learned if the game was fair or not. From what we found out, it is NOT fair.
Here are the pictures that we used in class (well something that I wrote down).



From the percents shown, you can obviously see that the opponent has a higher chance of winning. With 2 dice, there are 36 total possible outcomes (T.P.O. shown in the picture). Out of those 36 outcomes, the player has 6 chances to get points. Thus coming with the fraction 6 over 36 (6/36). Although, for the opponent he has 30 chances to get points. So of course, in the game the opponent mostly wins. When the player wins, it is mostly luck.


2. Racing Game



In class, Mr. Harbeck told us to make this game fair and unfair. This game lets us choose the chances for the red or blue to win. The way this game works is with a die. Which means there are six total possible outcomes. So if the game was to be fair, then the possibilities would look something like this :



That picture means, each player (red and blue) would have a 50% chance of winning.
If the game was unfair, then the chances for one of the players would be really low. An example for the game being unfair is something like this :



So now the percents of each player would be ..

From the percents, you can see that blue has a really good chance of winning.
(Be sure to write this down, because I think that this is homework.)


3. Probability Tree

Another thing that we did in class was a probability tree. The items/pictures we used were a coin (H/T) , a spinner with three sides (A,B,C) and another spinner but with 4 sides (A,B,C,D). Here is a picture of what we did.


(Thanks to Kim C., for the picture.)

To calculate the total possible outcomes you figure out the possible outcomes of the 3 objects.
For the coin there are 2 outcomes, for the spinner with 3 sides there are 3 outcomes and for the spinner with 4 sides there are 4 outcomes.
Thus .. 2 x 3 x 4 = 24.
Here is a picture for that equation :

(Thanks to Kim C., AGAIN for the picture)

Probability trees are a great way to show how you found the total possible outcomes.
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Im done, sorry for all the pictures I copied off of the other posts, I just didn't have time to make my own. Please tell me what I did good and what I did wrong, as it will help me to do better next time. That being said, the next scribe is .. -drum roll- JOSEPH!
Good luck to the next scribes!