Concept explainers
Figure 12.5 In pea plants, round peas (R) are dominant to wrinkled peas (r). You do a test cross between a pea plant with wrinkled peas (genotype rr) and a plant of unknown genotype that has round peas. You end up with three plants, all which have round peas. From this data, can you tell if the round pea parent plant is homozygous dominant or heterozygous? If the round pea parent plant is heterozygous, what is the probability that a random sample of 3 progeny peas will all be round?
To write:
The probability that a random sample of 3 progeny peas will be round.
Introduction:
The test cross can be defined as the cross, which is used to determine the genotype of the plants, especially, whether it is heterozygous dominant or homozygous dominant. In case the result of test cross comes as all dominant, then the plant is homozygous dominant, in case the cross shows 1:1 phenotype of dominant: recessive then the plant tested would be heterozygous dominant.
Explanation of Solution
The question says that a round seed pea plant was crossed with recessive (wrinkled seed) pea plant, which gives three plant having round pea seeds.
The given below is the analysis of the heterozygous pea plant and homozygous pea plant with a wrinkled plant.
From the crosses shown above, we can observe that in a test cross, the homozygous dominant plant produces all heterozygous dominant plants and the heterozygous plant produces 50% dominant and 50% recessive.
The transfer of the allele is random, as there is a probability that the plant with homozygous dominant trait would also produce the round seed, the data given in the question is very small. Hence, it cannot be concluded that the parent is homozygous or heterozygous. But, as per the given data one can most probably say it is homozygous.
For a heterozygote plant, the probability of getting one plant having round seed is 50% or ½.
Hence, the probability of getting 3 plant with a round seed with heterozygote plant would be:
The tested plant can be both homozygous or heterozygous and the probability of getting 3 plant with round seed by the heterozygous plant is 1/8.
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