Most Helpful Guy
Red hair is a recessive gene.
If one partner is brown haired, then that will be the dominant gene.
The only chance of having a red haired child, is if the brown haired parent carried the red haired gene recessively. In which case, the odds are 25% or 1 in 4 chance, that that red head gene will match the dominant gene of the ginger parent.
So the answer is 1:4, IF and only IF the brown haired parent carries the recessive ginger gene.