Wikipedia says that powerball is out of 69 balls, not out of 50, and in the U.S. there are only about 100 draws per week. I cant imagine the worldwide numbers are more than an order of magnitude higher (I guessed it at 200/week in a sibling comment). That’s 7.5x more potential draws, and 5x-35x fewer draws per week, which would change the numbers quite a bit, making the weekly chance way way lower than your estimate.