A recessive mother (rr) and a heterozygous father (Rr) start a family. What genotypes can their children have, and in what ratios?

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Mother can only have r gametes.  Father could have R or r gametes.  Place Father's gametes in column headings and use Mother's r as the start of the row.  You'll see the only combinations are Rr and rr.  1:1 ratio or 50% for each genotype.