That's not quite right. You need one 10 for the fact that you listened to ten songs yesterday, and another 10 for the fact that you're listening to ten songs today.
Assume that you got 10 unique songs yesterday, which is the case ~96% of the time. Then there are 990 songs you didn't hear yesterday, and for every song you listen to today, there is a 990/1000 chance that it's one of those songs. Hence the chance of only hearing new songs today is (990/1000)^10 = 90.4%.
Assume that you got 10 unique songs yesterday, which is the case ~96% of the time. Then there are 990 songs you didn't hear yesterday, and for every song you listen to today, there is a 990/1000 chance that it's one of those songs. Hence the chance of only hearing new songs today is (990/1000)^10 = 90.4%.