QuestionNeil has 181 songs on a playlist. He's categorized them in the following manner: 31 gospel, 20 blues, 36 classical, 24 rap, 16 rock, 9 pop, and 45 jazz. If Neil begins listening to his playlist on shuffle, what is the probability that the first song played is a classical song? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Studdy Solution
STEP 1
What is this asking? What are the chances that the first song Neil hears is classical music when his playlist is on shuffle? Watch out! Don't forget to simplify your fraction to the lowest terms!
STEP 2
1. Find the total number of songs.
2. Find the number of classical songs.
3. Calculate the probability.
STEP 3
We're given that Neil has a **whopping** songs in total!
This will be our **denominator**, representing all possible outcomes.
STEP 4
We know Neil has **glorious** classical pieces.
This will be our **numerator**, representing the favorable outcomes.
STEP 5
Probability is all about favorable outcomes divided by total possible outcomes.
So, we'll divide the number of classical songs by the total number of songs.
STEP 6
STEP 7
Since and don't share any common factors other than , the fraction is already in its **simplest form**!
We can also express this as a decimal rounded to the nearest millionth.
STEP 8
STEP 9
The probability that the first song played is a classical song is or approximately .
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