In
the PowerBall game, there are 53 white numbers, 26 even and 27
odd, from which to choose 5.
The probability of 2-4-6-8-10 appearing is actually lower than
say 1-2-5-6-7. Look closely at the number of odd and even
numbers.
Forget for a minute that 5 numbers are drawn. Consider drawing
just one number. At first, the odds of drawing an odd or even are
nearly equal with a slight advantage towards odd since there is
one extra odd number.
Odds/Probability of Drawing One Number
Odd: 1 in 1.96 or 50.9%
Even: 1 in 2.03 or 49.1%
Acknowledge that the ordering of the numbers is irrelevant to
the paytable. That is, the combination 1-2-3-4-5 is equal to
5-4-3-2-1.