Please help, I am not quite sure where to start.
Genes M and P are linked and are 30 map units apart. If genotype MP/mp is test crossed, what is the probability that the progeny will be homozygous recessive for both genes?
What is the chance of producing a gamete that is MP in genotype MP/mp (same 30 map units apart)?
To answer both of your questions, we need to understand a few concepts related to genetic linkage and recombination.
First, let's discuss genetic linkage. Genes that are located close to each other on the same chromosome are said to be linked. Linked genes tend to be inherited together unless recombination occurs during meiosis, which is the process of forming gametes (sperm and egg cells). The frequency of recombination between two genes is measured in units called map units or centimorgans (cM).
In your case, genes M and P are linked and are 30 map units apart. This means that there is a 30% chance of recombination occurring between them during meiosis.
Now, let's move on to the first question: What is the probability that the progeny will be homozygous recessive for both genes (genotype mp/mp) when genotype MP/mp is test crossed?
In a test cross, an individual with an unknown genotype (MP/mp) is crossed with a homozygous recessive individual (mp/mp). The purpose of a test cross is to determine the unknown genotype of the individual being tested. In this case, we want to find the probability of getting progeny with the genotype mp/mp.
Since genes M and P are linked, the chance of recombination between them is 30%. Therefore, there is a 30% chance that the individual's gametes will undergo recombination to produce a recombinant gamete with the genotype mp. Conversely, there is a 70% chance that the gametes will remain non-recombinant with the genotype MP.
To calculate the probability of getting progeny with the genotype mp/mp, we multiply the probabilities of obtaining the recombinant gamete (30%) with itself (30%). Thus, the probability is 0.3 * 0.3 = 0.09, or 9%.
Now, let's address the second question: What is the chance of producing a gamete that is MP in the genotype MP/mp?
In individuals with the genotype MP/mp, the gametes can either be non-recombinant (MP) or recombinant (mp) due to the possibility of recombination between the linked genes M and P.
We know that the chance of recombination between these genes is 30%. Therefore, there is a 30% chance of producing a recombinant gamete with the genotype mp. Conversely, there is a 70% chance of producing a non-recombinant gamete with the genotype MP.
To summarize, the chance of producing a gamete that is MP in the genotype MP/mp is 70%.