Renae has programmed her music player to play all five songs in her playlist in a random order without repeating songs.

1. What is the probability that the first song is a country song?

   Hint (a):

   The probability that the first song is a country song is:

   $\frac{\text{# of country songs}}{\text{total # of songs}}$

2. If the first song is a country song, does that affect the probability that the second song is a country song? Explain your thinking.

   Hint (b):

   How does eliminating one country song from the playlist affect the probability of the second country song playing next?

3. As songs are playing, the number of songs left to play decreases. Therefore, the probability of playing each of the remaining songs depends on which songs have played before it. This is an example of events that are not independent. If Renae has already listened to “Don’t Call Me Mama”, “Carefree and Blue”, and “Smashing Lollipops”, what is the probability that one of the singers of the fourth song will be Sapphire? Explain your reasoning.

   Hint (c):

   How many songs by Sapphire are remaining compared to the total number of songs left?

   Answer (c):

   $\frac{1}{2}$

   Only two songs are left and only one of them is sung by Sapphire.

4. To get home, Renae can take one of four buses: #$41$, #$28$, #$55$, or #$81$. Once she is on a bus, she will randomly select one of the following equally likely activities: listening to her music player, writing a letter, or reading a book. Her choice of bus and her choice of entertainment are independent events, because the bus that Renae takes does not affect which activity she chooses. For example, what is the probability that Renae writes a letter if she takes the #$41$ bus? What is the probability that Renae writes a letter if she takes the #$55$ bus?

   Hint (d):

   Does the bus choice affect the activity she performs?

   More Help (d):

   $\frac{\text{# of activities she does}}{\text{total # of activities available}}$