Step 1: Understanding the problem.
T.H. Morgan studied the inheritance of two traits: wing type (normal or vestigial) and body color (gray or black) in Drosophila. We are asked to find the expected ratio of flies with vestigial wings and gray bodies in the F\(_2\) generation.
Step 2: Applying Mendelian genetics.
- Vestigial wings (vg) are recessive, normal wings (VG) are dominant.
- Gray body (G) is dominant, black body (g) is recessive.
- F\(_2\) generation from dihybrid cross (heterozygotes) produces 16 combinations.
- The combination for vestigial wings (vg/vg) and gray body (G/-) occurs in 3 out of 16 offspring.
Step 3: Conclusion.
The ratio of vestigial winged, gray body flies in F\(_2\) is \(3/16\).