If your MP3 player has 5000 songs and the player is set to true random what are the odds it will play the same song 5000 times in a row?

Answer 1

P(song playing once) = 1/5000

P(song playing 5000 times) = P(song playing once)5000 = (1/5000)5000

[ P(something) means the probability of that something happening. Since each song is equally likely, the probability is 1 over the number of songs. The probability of the song playing multiple times is that same probability multiplied by itself however many times it plays. So, for 5000 times, it's that probability to the 5000th power.

As for the size of the answer, it's incredibly tiny. P(once) = 0.0002 or (2) / (10000). So, every time you multiply, you usually add on four zeros. However, sometimes the power of two in the numerator will increase the number enough to decrease the number of zeros by one. So, best guess, (locked my computer up trying to compute it, haha), somewhere between 15,000 and 20,000 zeros, probably closer to the latter. ]

Many thanks for responding. Any chance of expanding on that in layman's terms. Also how huge a number is your conclusion i.e. how many zeroes in it.

Hopefully Yours

Bill