The odds of anyone winning the $150 million Powerball draw ...
134.5 million to 1

The calculation: you pick 7 numbers and these need to match all 7 drawn from the main 35 balls. This lands you a Division 2 prize. If you also then match the 1 additional (out of 20 options) Powerball, this becomes the Division 1 jackpot.
So, for the first ball, you have 7 chances out of 35 to match a number.
For the second ball, you have 6 remaining chances out of 34 remaining to match a number.
For the third ball, you have 5 remaining chances out of 33 remaining to match a number... etc
For the seventh ball, you have 1 remaining chances out of 29 remaining to match a number.
Source: Stephen Woodcock, Associate Professor of Mathematical Sciences, University of Technology Sydney