Question

the gene for red hair is recessive to the gene for black hair

Answer 1

genotype of black hair BB
genotype of red hair bb
here is an example :

Father (BB) Mother (bb)
\ /
\__________/
|
child (Bb)

So, the child will have black hair since it is dominant but will also receive the (recessive) red hair trait but will not be expressed.

hope this helped
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Answer 2

The Gene for red colored hair is recessive to that of Gene for black colored hair. So to be a person of red colored hair, the Genotype of person must be homozygous recessive that is bb.
To be a person of black colored hair the Genotypes may be BB or Bb.
If one parent is of black colored hair with homozygous dominant Genotype and other parent of red colored, then:-
BB x bb --> Their all children will be of black colored hair and are carrier of red colored Gene.The genotype of all children will be Bb.
If one parent is heterozygous for black colored hair and other parent is of red colored, Then:-
Bb x bb---> The probability of their children to be of black colored hair (Bb) and red colored hair(bb) will be 0.5 of each or 50% of each. Hope it helps.