You roll two standard number cubes. What is the probability that sum is odd, given than one of the number cubes shows a 4?

If one is already rolled as a 4, then there are only 6 other total combinations to get.

so what are sums to get an odd number?

4+1=5

4+3=7

4+5=9

so you have a 1/3 chance of getting an odd number, given that one of the dice is already a 4.