In a Mendelian dihybrid cross, a true-breeding pea plant with...

In pea plants, inflated pod shape is dominant over constricted pod shape, and green pod color is dominant over yellow pod color.

Let the alleles for pod shape be $I$ (inflated)$and i$ (constricted), and for pod color be $G$ (green)$and g$ (yellow).

The true-breeding parents are $IIGG$ (inflated green)$and iigg$ (constricted yellow).

The $F_{1}$ offspring will all be heterozygous $IiGg$, exhibiting the inflated green phenotype.

When the $F_{1}$ generation is self-pollinated ($IiGg \times IiGg$), the $F_{2}$ progeny will show a standard dihybrid phenotypic ratio of $9:3:3:1$.

The phenotypes corresponding to this ratio are:
$\dfrac{9}{16}$ Inflated green pods
$\dfrac{3}{16}$ Inflated yellow pods
$\dfrac{3}{16}$ Constricted green pods
$\dfrac{1}{16}$ Constricted yellow pods

Therefore, the proportion of $F_{2}$ progeny with inflated yellow pods is $\dfrac{3}{16}$.

Answer: $\dfrac{3}{16}$