What are the chances of ever winning the 2nd place prize for PB or MM?

I didn't say the odds on the charts were INCORRECT, I said "who knows how they figure them".

"The odds of matching the five white balls ONLY are 5,153,633 to 1, because you have to multiply the total number of white ball combinations by 35/34, as the odds of NOT hitting the bonus ball are 34/35."

If you multiple 5,006,386 (the number of combos in a 5/59 matrix) by "35/34" you get 5,153,633. That I understand, but how do they get the figure 1 in 55?

They figure the odds using the only formula there is for calculating the number of combinations.

They get the 1 in 55 figure by multiplying the chance of getting the power ball (1/35) by the chance of matching 0 of 59. The latter is 1-(chance of matching 5)-(chance of matching 4)-(chance of matching 3)-(chance of matching 2)-(chance of matching 1), which is about 1/1.6.

I didn't say the odds on the charts were INCORRECT, I said "who knows how they figure them".

Actuall the odds are calculated the only way that makes sense. 

First, the total number of possible combinations is calculated, then the number of winning combinations for each level are calculated and to get the odds of winning at each level, the numbers of winning combinations at each level are divided by the number of possible combinations.

 possible combos of 5/59 + 1/35 numbers = 175223510
 MATCH    ODDS            WINNING COMBOS  ODDS 1 CHANCES
 5/5+B   1 : 175223510      1              1 : 175223510
 5/5+0   1 : 5153633        34             1 : 5153633
 4/5+B   1 : 648976         270            1 : 648976
 4/5+0   1 : 19088          9180           1 : 19088
 3/5+B   1 : 12245          14310          1 : 12245
 3/5+0   1 : 360            486540         1 : 360
 2/5+B   1 : 706            248040         1 : 706
 1/5+B   1 : 111            1581255        1 : 111
 0/5+B   1 : 55             3162510        1 : 55
 ____________________________________________________________
 overall odds 1 : 31.8