A purple pea plant could be PP or Pp. Both look the same, so looking will not tell you. In Monohybrid Crosses we went from genotypes to offspring. A test cross runs that idea backward: from offspring to a hidden genotype.
Key idea
Cross the unknown dominant-looking organism with a homozygous recessive (pp) one. If any offspring show the recessive trait, the unknown was Pp. If many offspring all show the dominant trait, the unknown is almost surely PP.
Why it works
The pp parent can give only p, so it never hides anything: each offspring shows whatever allele came from the unknown parent. A PP parent gives only P, so every offspring is Pp and purple. A Pp parent gives p half the time, so about half the offspring are pp and white.
Worked example: Reading a result
A black guinea pig (black is dominant) is crossed with a brown one. The litter has 3 black and 2 brown pups. What is the black parent's genotype?
- The brown parent is bb and gives only b.
- A brown pup is bb, so it got b from the black parent too.
- So the black parent carries b.
Answer: Bb.
Worked example: How sure can we be?
A Pp plant is test-crossed and gives 5 offspring. What is the chance that all 5 are purple just by luck?
- Each offspring of Pp × pp is purple with chance ½.
- Offspring are independent, so multiply: ½ × ½ × ½ × ½ × ½.
Answer: $\left(\frac{1}{2}\right)^5 = \frac{1}{32}$, about 3%. With 10 offspring it is $\frac{1}{1024}$.
Common mistake
Two errors. First, crossing the unknown with a dominant-looking organism: a PP partner hides the result, because every offspring gets a P from it. Second, deciding "PP" from only two or three purple offspring. A Pp plant gives all-purple small litters fairly often; more offspring make the answer more certain.
One recessive offspring settles it: the unknown is heterozygous. All-dominant offspring never prove PP; they only make Pp less and less likely.