9.3 Two Counting Principles

9.3 Two Counting Principles
Hello everyone!
What we learned in class today had a lot to do with terminology and ways to interpret what the question's trying to ask. So let's get started!

• Independent Events--> The way one event occurs doesn't affect the way the other could occur.
  
  In class, we used the example of a 3 day summer camp. On the first day, the students were allowed to pick one Outdoor Activity to do in the morning and one Indoor Activity to do at night. What they chose in morning did not affect what they did at night. Therefore, this situation is an example of independent events.
  
  Another example is what the campers eat for meals. What they ate for breakfast won't affect what they eat for lunch or dinner (unless they're sick of the same old thing).
  


• Dependent Events--> The way one event occurs affects the way the other could occur.
  
  Next day at camp, it rained so none of the outdoor activites were available. The campers could pick any indoor activity to do but what they did in the morning could not be repeated in the afternoon.
  
  Another example is usage of showers. If the campers were only allowed to take one shower a day, then a person who showered in the morning will not be able to take one later at night. (Oh no! Surprised?)
  


• Mutually Exclusive Events--> The occurrence of one event excludes the possibility the other will occur. (choose one, can't do the others)
  
  The last day at camp is only a half day so the campers can only pick one activity to do. Once they pick the activity, the other choices are gone.
  
  Another example is choosing an outfit for the day. Once a camper makes a decision between flip flops and converse, she's not going to be able to wear the other pair of shoes also. Therefore, this is a mututally exclusive event.

Properties of the Events

1. Let A and B be two events that occur in a sequence.

n(A+B)= n(A) * n(B/A) for dependent events

n(A+B)= n(A) * n(B) for independent events (there's no overlap!)

'A' is the number of ways an event can occure while 'B' is the number of ways an event can occur if 'A' occurs.

2. Overlapping Events: When choices in an event overlap or repeat.

Suzy is trying to decide what kind of frozen yogurt she should eat and what topping to put on. She can choose between chocolate, vanilla, and regular frozen yogurt with choice of granola, blueberries, strawberries, pineapple pieces, reese's, or nothing as a topping. How many choices does she have for either vanilla frozen yogurt or toppings of blueberries or granola? Let's make a table!

As you can see from my paint picture, there is an overlap in the toppings (in bold) and vanilla yogurt (in italics). Two x's are bold and italics. Therefore, to figure out this problems, you must do this:

n (A or B)= n(A) + n(B) -n (A~B)
~=it's supposed to look like a bump or a concave down mini parabola but this is the closest I could get. It means "and" or the intersection of A and B.

so 3+6-2=7 There's 7 choices Suzy has.

If you're still confused about all this stuff, you can check out this website (but I think there's more than we learned on this website lol):
http://www.richland.edu/james/lecture/m116/sequences/counting.html

Before I go, here's a picture of my sword dance team that performed at the Dorothy Chandler Pavilion on Christmas Eve. The Christmas program we were a part of airs on PBS or whatever channel you get Sesame Street on every Christmas and Christmas Eve. I was part of an interview but sadly running behind schedule made them cut it from the show. Oh well. This year, we're doing 3 drum dance (which I am also going to do for JPD!):

Claire, you're up next!!!