Hello. I have the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

Let's say you have 354 songs in your entire music library. And let's say you started playing those songs, in shuffle mode, starting from the very first (random) song. Assuming perfect randomization, let's say you are now on the 34th random song in your shuffle. If you have one specific favorite song in your entire library, what is the probability that your specific favorite song is selected either as the 34th songor earlier?

I calculated the probability as follows:

(1/354) + (353/354)(1/353) + (353/354)(352/353)(1/352) + ... + (353/354)(352/353)(....)(325/326)(1/325)

Simplification of terms leads to (1/354) + (1/354) + (1/354) + ... + (1/354)

..which in turn leads to 34(1/354) = (34/354).

Was this probability value calculated correctly?

(In case you're wondering, the method I used was to add all of the probabilities of selecting your favorite song at each specific shuffle count. Each grouping of parentheses represent each individual probability, and the third grouping, for example, was the probability that the favorite song did not come up on either of the first two songs butdidcome up on the third song).

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# Shuffling Songs probability question

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