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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. Homework Help
a. 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?
b. Are each of the combinations of two songs equally likely? Why is that important?
c. Find the probability that Renae will listen to two songs with the name "Mama" in the title.
d. What is the probability that at least one of the songs will have the name "Mama" in the title?
e. Why does it make sense that the probability in part (d) is higher than the probability in part (c)?
PLAYLIST
a. I Love My Mama (country)
by the Strings of Heaven
b. Don't Call Me Mama (country) Duet
by Sapphire and Hank Tumbleweed
c. Carefree and Blue (R & B)
by Sapphire and Prism Escape
40²
d. Go Back To Mama (Rock) Duet
by Bjorn Free and Sapphire
e. Smashing Lollipops (Rock)
by Sapphire

User Chime
by
8.2k points

2 Answers

3 votes

Answer:

a. 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?

Explanation:

CPM EDUCATIONAL PROGRAM

hope this helps!!

User Egorgrushin
by
8.1k points
6 votes

10 song combinations, equally likely. 90% chance of "Mama" song, due to more pairing possibilities.

Analyzing Renae's MP3 Player Playlist

a. Sample Space:

Since the order of songs doesn't matter, we can create the sample space by listing all unique combinations of two songs:

1. I Love My Mama - Don't Call Me Mama

2. I Love My Mama - Carefree and Blue

3. I Love My Mama - Go Back To Mama

4. I Love My Mama - Smashing Lollipops

5. Don't Call Me Mama - Carefree and Blue

6. Don't Call Me Mama - Go Back To Mama

7. Don't Call Me Mama - Smashing Lollipops

8. Carefree and Blue - Go Back To Mama

9. Carefree and Blue - Smashing Lollipops

10. Go Back To Mama - Smashing Lollipops

We can be sure we listed all combinations by systematically pairing each song with every other song once, ensuring no song is repeated or left out.

b. Equal Likelihood:

Yes, each combination of two songs is equally likely. This is because the MP3 player randomly selects songs without any bias. Each song has an equal chance of being chosen first, and then the second song is chosen with equal probability from the remaining songs.

This equal likelihood is crucial for calculating probabilities in the following parts.

c. Probability of "Mama" Songs:

There are 3 songs with "Mama" in the title: I Love My Mama, Don't Call Me Mama, and Go Back To Mama. We need to find the probability of selecting 2 songs where at least one has "Mama".

There are 3 ways to select one "Mama" song and 4 ways to choose the second song (any of the remaining songs). However, we've overcounted 3 combinations (each "Mama" song paired with itself). Therefore, the total favorable outcomes are (3 * 4) - 3 = 9.

The probability is then the number of favorable outcomes divided by the total number of outcomes (10): 9/10 = 0.9.

d. Probability of at least one "Mama" Song:

We can find this probability by considering the opposite event: the probability of NO "Mama" songs being selected. There's only 1 way to achieve this (picking Carefree and Blue with Smashing Lollipops).

Therefore, the probability of at least one "Mama" song is 1 minus the probability of no "Mama" songs: 1 - 1/10 = 9/10.

e. Higher Probability for at least one "Mama" Song:

The probability of at least one "Mama" song being higher than the probability of exactly two "Mama" songs makes sense because there are more ways for at least one "Mama" song to occur. There are 3 "Mama" songs, and each can be paired with any of the 4 non-"Mama" songs, resulting in 12 possible outcomes.

However, for exactly two "Mama" songs, we only have 3 ways to choose the first "Mama" song and then 2 ways to choose the second (since we can't pick the same one again). This results in only 6 possible outcomes.

Therefore, there are twice as many ways for at least one "Mama" song to occur compared to exactly two, justifying the higher probability in part (d).

User Seawolf
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8.4k points