To accomplish the screening, researchers synthesize a single-stranded dna probe using vgp mrna as a template. what will be the sequence of nucleotides in the probe?

There are only two things you need to know. 

1. A probe works by base pairing to the DNA strand, so its sequence must be complementary to the DNA sequence of interest. 
2. You need to know which strand is the strand of interest. 

To tell the truth I'm not sure about the answer to question 2. Which one is the template strand? Either can be used as the template. I *think* the top strand is typically used as the template, but usually it's specified. Perhaps it's specified somewhere in your question or previously. 

Anyway once you find your template strand, an mRNA was made from it so its sequence is complementary to the template strand. Then a probe was made using the mRNA as a template, so it is complementary to the mRNA, which in turn is complementary to the template strand (on the original DNA). So essentially what this means is that the probe will have the same sequence as the DNA template strand (the one you used to make the mRNA).

Diagrams for sure 67(8? ; 4