I was always useless at maths.
I have 1000 songs on my playlist. I randomly play 100 songs a month (this can include the song being played more than once).
What is probability that I will not play one particular song at all during the year?

Nil, because the shuffling algorithm isn’t really random

Just 3 weeks ago, when sitting maths exam at uni, I could have gave you an answer.

It’s now gone.

‘S how I roll.

If the algorithm is truly random, then you have a 90% chance of not playing it each month.

0.9 x 0.9 x 0.9 twelve times.= 0.3 ish so 30% chance of not playing it in a year.

Also nil if the particular track is something your eight year old daughter put on there.

Matt

It’s higher than that smudger as you could play the same track multiple times each month. My guess is .999 times .999, 100 times, then multiply by twelve for each month.

Matt

In theory, the chances of a track not being played in a month is 9/10.
The chances of a track not being played in 12 months is 9/10^ 12, or about 28%, apparently.

Assuming the shuffle is entirely random, of course.

Smudger, You’re assuming it plays 100 different songs per month. Surely it’s 0.999 per play rather than 0.9 per month…

In fact, I think the months are irrelevant. It’s 1200 random songs per year so 0.999^1200 = 30.1%

Might be wrong though….

Yup – missed the bit that they can be repeated in a month.

If I remember correctly:
When sample n times from the set {1,…,x}, then the expected number of unique values is x[1−(1−1/x)^n]

In one month the number of unique songs should be 95.207852886. So 4.8ish repeats.

In 12 months I think: 698.986570907 unique songs – 302 ish repeats.

I’m too old for this stuff!

#Edit – the ‘power of n’ in the formula got lost

In fact, I think the months are irrelevant. It’s 1200 random songs per year so 0.999^1200 = 30.1%

Gets my vote

What is probability that I will not play one particular song at all during the year?

Answer = unlikely.

But it’s also possible the same song could repeatedly play non-stop for the next year.

Just don’t walk down Easy Street.

If this is a Spotify playlist, my experience suggests that it is considerably more likely to play songs at the end of your playlist than at the beginning. I haven’t heard some of the ones near the start for ages.

Nil, because the shuffling algorithm isn’t really random

None, because Spotify’s shuffling algorithm doesn’t work properly.

Just don’t walk down Easy Street.

*Shoots Glenn with crossbow*