To Driftwood,
The odds are calculated by dividing the all the possile winning combinations by all the possible combinations. For example in Powerball there are 120,526,770 possible combinations and only one combination with 5 winning numbers and the powerball for the jackpot ,so the odds of winning the jackpot is 1:120,526,770 and for 5 winning numbers and no powerball, there are 41 combinations left or 41:120,526,770 = ~1:2,939,677 and etc. To get the odds for the rest of the combinations ,you have to calculate the number of winning combination for each conditions. Below are calculations for each situations for both Powerball and Magamillions.
name of game : POWERBALL
size of combination 5
amount of numbers in group 53
amount of bonus numbers 42
possible combinations of 5 of 53 with 1 of 42 bonus numbers is 120,526,770
MATCH ODDS WINNING COMBINATIONS
5 / 5 +B 1 : 120526770 1
5 / 5 1 : 2939677 41
4 / 5 +B 1 : 502195 240
4 / 5 1 : 12249 9840
3 / 5 +B 1 : 10685 11280
3 / 5 1 : 261 462480
2 / 5 +B 1 : 697 172960
1 / 5 +B 1 : 124 972900
0 / 5 +B 1 : 70 1712304
odds of a prize 1 : 36
total possible combos 120526770 total winning combos 3342046
name of game : MEGAMILLONS
size of combination 5
amount of numbers in group 52
amount of bonus numbers 52
possible combinations of 5 of 52 with 1 of 52 bonus numbers is 135,145,920
MATCH ODDS WINNING COMBINATIONS
5 / 5 +B 1 : 135145920 1
5 / 5 1 : 2649920 51
4 / 5 +B 1 : 575089 235
4 / 5 1 : 11276 11985
3 / 5 +B 1 : 12502 10810
3 / 5 1 : 245 551310
2 / 5 +B 1 : 833 162150
1 / 5 +B 1 : 152 891825
0 / 5 +B 1 : 88 1533939
odds of a prize 1 : 42.7 1 : 42.7
total possible combos 135145920 total winning combos 3162306
Hope this helps, good luck to you
RJOh