A radio station has two tickets to give away to a Beyonce concert. It held a contest and narrowed the possible recipients down to four people: Alyssa (A), Mackenzie (M), Crystal (C),
and Grace (G). The names of two of these four will be
selected at random from a hat and the
two people will be awarded the tickets.
1. Use the counting principle to determine the number of points in the sample space.
2. Construct a tree diagram and list the sample space.
3. Determine the probability that Mackenzie is selected.
4. Determine the probability that Alyssa is not selected.
5. Determine the probability the neither Grace nor Crystal are selected.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?