Title: How Can We Show Sample Spaces with Diagrams?

Visualizing sample spaces helps us understand what might happen in probability experiments. A sample space is just a list of all the possible outcomes from an experiment.

Types of Diagrams:

1. Tree Diagrams:

   • These are great for showing experiments that happen step by step.
   • Each line on the tree shows a possible outcome.
   • For example, if you toss a coin twice, the possible outcomes are {HH, HT, TH, TT}. You can draw this out using a tree.

2. Venn Diagrams:

   • These help us see how different events are connected.
   • We use circles to show events, and where they overlap shows outcomes that they share.
   • For example, if you roll a die, the event of rolling an even number can be shown as a circle inside the sample space of {1, 2, 3, 4, 5, 6}.

3. List Representation:

   • We can also write out the possible outcomes in a list.
   • When rolling two dice, the sample space is {(1,1), (1,2), ..., (6,6)} which means there are 36 different outcomes.

Using these diagrams makes it easier to understand tricky situations. This way, we can calculate probabilities and look at data more clearly.