Hi Everyone!
So the first week of classes wasn't that bad at all. It's my last semester at Mesa Community College and I feel very confident about the semester and how it plays out. The first week of MAT257 wasn't that bad! We are learning about probability. The first lesson started off in Probability in the textbook. In the first lesson, we first learned the definitions of experiment, outcome, sample space, and event. I thought those were really common words but they mean different things in math. The definitions are:
Experiment: An activity whose results can be observed and recorded.
Outcome: Each of the possible results of an experiment.
Sample Space: A set of all possible outcomes for an experiment.
Event: Any subject of a sample space.
The first example of the notes was pretty simple and it gave me an idea of what the whole chapter was going to be about (so I thought). The example read:
Suppose an experiment consists of drawing 1 slip of paper from a jar containing 12 slips of paper, each with a different month of the year written on it. Find each of the following:
a. The sample space S for the experiment. The answer was S = {January, February, March, April, May, June, July, August, September, October, November, December}.
b. The event A consisting of outcomes having a month beginning with J. The answer was A = {January, June, July}.
c. The event B consisting of outcomes having the name of a month that has exactly four letters. The answer was B = {June, July}.
d. The event C consisting of outcomes having a month that begins with M or N. The answer was C = {March, May, November}.
Then, further in the lesson, there were a few more definitions we had to know. Some of them were experimental (empirical) probability, theoretical probability, and equally likely. I didn't know what experimental probability or theoretical probability were before and so I wrote the definition down to make sure I can remember it that way. The definitions were:
Experimental (empirical) Probability: Determined by observing outcomes of experiments.
Theoretical Probability: The outcome under ideal conditions.
Then, after that, we learned the "Law of Large Numbers" which is the Bernoulli's Theorem. The definition of that was:
"As the number of trials of an experiment increases, the experimental or empirical probability of a particular event approaches a fixed number, the theoretical probability of that event."
Last, we learned about mutually exclusive and non-mutually exclusive events. The definition of mutually exclusive event is:
"Events A and B are mutually exclusive if they have no elements in common."
To figure out if the events are mutually exclusive, you have to find the sum of the probabilities with the union. An example would be if we had a spinner with 0-9 numbers on it. We would consider one spin of the wheel. The sample space would be S = {0,1,2,3,4,5,6,7,8,9}. Event A would be A = {0,1,2,3,4} and Event B would be B = {5,7}. Each event doesn't have the same numbers, so they are mutually exclusive.
In addition to learning probability with numbers, we learned about Geometric Probability or otherwise known as the Area Model. This means that the probability model that uses geometric shapes is the area model. When Area Model is used to determine probabilities geometrically, outcomes are associated with points chosen at random in a geometric region that represents a sample space. An example of this would be tossing a coin. There would be a box with heads on one diagonal side and tails on the other side.
What I found online was a really cool link to help kids with probability! Check it out: Probability for Kids! .
