Eddie is arguing with Tana about the probabilities of different outcomes when flipping three coins. They decide to flip a penny, nickel, and a dime.

1. Which would be better for representing the sample space, a systematic list, a tree diagram, or an area model? Justify your answer.

   Hint (a):

   There are three coins. Can you represent the outcomes of flipping three coins with a systematic list? An area model? A tree diagram?

   Answer (a):

   Tree diagram, but why?

2. Determine the sample space of all possible outcomes. How many outcomes are there?

   Answer (b):

   

3. Calculate the probability of each of the following events occurring. Be sure to show your thinking clearly.

   Hint (c):

   Use the diagram from part (b) to answer parts (i) through (iv).

4. Which is more likely, flipping at least two heads or at least two tails? Explain.