Let's solve each part step by step, with explanations after each step. --- ## **Step 1: Determine the Genotypes and F1 Cross** ### **Genetic Information** - **Color:** Orange (R) is dominant to red (r). - **Spot Size:** Large spots (L) are co-dominant with small spots (l), so **dotted (Ll)** and **spotted (LL or ll)**. - **Texture:** Dense (T) is dominant to brittle (t). ### **Parental Cross** - **Parent 1:** Orange, dotted, dense (must be **Rr Ll Tt**) - **Parent 2:** Orange, spotted, brittle (must be **Rr LL tt** or **Rr ll tt**) Let’s assume **Parent 2** is **Rr ll tt** for small-dotted lentil (as per image b). #### **F1 Generation** - Cross: **Rr Ll Tt** × **Rr ll tt** ### **F1 Gametes and Ratios** - Color: \( Rr \times Rr \rightarrow \frac{3}{4} \) Orange, \( \frac{1}{4} \) Red. - Spots: \( Ll \times ll \rightarrow \frac{1}{2} \) Ll (dotted), \( \frac{1}{2} \) ll (spotted). - Texture: \( Tt \times tt \rightarrow \frac{1}{2} \) Tt (dense), \( \frac{1}{2} \) tt (brittle). **Explanation:** We determined the genotypes for each trait and their resulting proportions in the F1 generation, using basic Mendelian genetics. --- ## **Step 2: F2 Generation and Answering the Questions** ### **F2 Cross** - The F1 plants are selfed or intercrossed. Let's use their genotypes for F2 proportions: #### **a. What proportion of progeny will be orange, only spotted, and dense?** - **Orange**: \( \frac{3}{4} \) (from Rr × Rr) - **Only spotted:** "Only spotted" means **ll** (since Ll is "dotted," and LL or ll is "spotted"). - From Ll × ll: \( \frac{1}{2} \) Ll (dotted), \( \frac{1}{2} \) ll (spotted) - **Dense:** \( \frac{1}{2} \) (Tt × tt → \( \frac{1}{2} \) Tt (dense), \( \frac{1}{2} \) tt (brittle)) **Multiply the probabilities:** - \( \frac{3}{4} \) (orange) × \( \frac{1}{2} \) (spotted) × \( \frac{1}{2} \) (dense) - \( = \frac{3}{16} \) **Explanation:** We multiplied the individual probabilities for each trait to find the overall proportion for plants that are orange, only spotted, and dense. --- #### **b. Out of 300 progeny, how many will be dotted-spotted?** - **Dotted-spotted**: This refers to heterozygotes (Ll) for spot size. - From Ll × ll: \( \frac{1}{2} \) will be Ll (dotted), \( \frac{1}{2} \) will be ll (spotted) So, **dotted (Ll): \( \frac{1}{2} \) of total progeny**. - \( 300 \times \frac{1}{2} = 150 \) **Explanation:** Since half of the F2 progeny will be dotted (Ll), we multiply the total number by \( \frac{1}{2} \) to get the number. --- ## **Final Answers** ### **a. Proportion of progeny that will be orange, only spotted, and dense:** **\(\boxed{\frac{3}{16}}\)** ### **b. Out of 300 progeny, how many will be dotted-spotted?** **\(\boxed{150}\)**