Ali has 250 songs on her MP3 player. Of those, 150 are dance songs, 50 are R&B songs, and 30
songs are both dance and R&B.
1) when Ali has her player on shuffle, what are the odds in favour of her hearing a dance song that is not an R&B song?
2) what are the odds against her hearing a song that is both dance and R&B?
First of all, 150 + 50 + 30 ≠ 250
With that:
1) 50/250 = ?
2) 1 - 30/250 = ?
To answer these questions, we need to use the concept of probability. Probability is the likelihood of an event occurring. In this case, we want to calculate the probability of certain songs playing on Ali's MP3 player when it's on shuffle.
1) To find the odds in favor of Ali hearing a dance song that is not an R&B song, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The number of dance songs that are not R&B can be calculated by subtracting the number of songs that are both dance and R&B from the total number of dance songs: 150 - 30 = 120.
The total number of possible songs that can play on Ali's MP3 player is 250.
Therefore, the odds in favor of Ali hearing a dance song that is not an R&B song can be calculated as follows:
Odds in favor = Number of favorable outcomes / Total number of possible outcomes
= 120 / 250
So, the odds in favor of Ali hearing a dance song that is not an R&B song are 120/250.
2) To find the odds against Ali hearing a song that is both dance and R&B, we again need to determine the number of favorable outcomes and the total number of possible outcomes.
The number of songs that are both dance and R&B is given as 30.
The total number of possible songs that can play on Ali's MP3 player is still 250.
Therefore, the odds against Ali hearing a song that is both dance and R&B can be calculated as follows:
Odds against = Number of unfavorable outcomes / Total number of possible outcomes
= (Total number of possible outcomes - Number of favorable outcomes) / Total number of possible outcomes
= (250 - 30) / 250
So, the odds against Ali hearing a song that is both dance and R&B are 220/250.