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4-53.

For the evening, Renae has programmed her MP3 player to play all five songs in a random order.

 PLAYLISTI Love My Mama (country) by the Strings of HeavenDon’t Call Me Mama (country) Duet by Sapphire and Hank TumbleweedCarefree and Blue (R & B) by Sapphire and Prism EscapeGo Back To Mama (Rock) Duet by Bjorn Free and SapphireSmashing Lollipops (Rock) by Sapphire
1. What is the probability that the first song is a country song?

The probability that the first song is a country song is: $\large\frac{\text{# of country songs}}{\text{total # of songs}}$

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.

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

1. As songs are playing, the number of songs left to play decreases. Therefore, the probability of playing each of the remaining songs is dependent on which songs that have played before it. This is an example of events that are dependent events. 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.

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

$\frac{1}{2}$

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

2. In problem 4-51, you considered a situation of independent events, when the bus that Renae took did not affect which activity she chose. For example, what is the probability that Renae writes a letter if she takes the $\#41$ bus? What if she takes the $\#55$ bus?

Does the bus choice affect the activity she performs?

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