CPM Homework Help : CCG Problem 1-87

While waiting for a bus after school, Renae programmed her MP3 player to randomly play two songs from her playlist, below. Assume that the MP3 player will not play the same song twice.

A sample space is a list of all possible outcomes for a probabilistic situation. List the sample space for all the combinations of two songs that Renae could select. The order that she hears the songs does not matter for your list. How can you be sure that you listed all of the song combinations?
Answer (a):
10 combinations. a & b, a & c, a & d, a & e, b & c, b & d, b & e, c & d, c & e, d & e
Are each of the combinations of two songs equally likely? Why is that important?
Answer (b):
Yes. If the outcomes are equally likely, we can use the theoretical probability computation in the Math Notes box in Lesson 1.2.1.
Find the probability that Renae will listen to two songs with the name “Mama” in the title.
Answer (c):
$\frac{3}{10}$
What is the probability that at least one of the songs will have the name “Mama” in the title?
Answer (d):
$\frac{9}{10}$
Why does it make sense that the probability in part (d) is higher than the probability in part (c)?
Answer (e):
The outcomes that satisfy part (c) include the outcomes that satisfy (b), but there are others on the (c) list as well.

PLAYLIST

I Love My Mama (country)
by the Strings of Heaven
Don’t Call Me Mama (country) Duet
by Sapphire and Hank Tumbleweed
Carefree and Blue (R & B)
by Sapphire and Prism Escape
Go Back To Mama (Rock) Duet
by Bjorn Free and Sapphire
Smashing Lollipops (Rock)
by Sapphire