Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
The blood group of the mother is A+ and that of the father is AB+. Which of the
following statements is/are correct?
Options:
(A) Probability of the offspring with A+ blood group is 0.5
(B) Probability of the offspring with AB+ blood group is 0.125
(C) Probability of the offspring with B+ blood group is 0.125
(D) Probability of the offspring with O+ blood group is 0.375
Official Answer Key:
A;C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2025 Q.53)**
**1. Governing Concept**:
- **Topic**: Classical Genetics & Human ABO and Rh Blood Group Inheritance
- **ABO System**:
- Mother is Blood Group A: Genotype can be $I^A I^A$ or $I^A i$.
- Father is Blood Group AB: Genotype is $I^A I^B$.
- Possible child genotypes:
- If mother is $I^A I^A$: $I^A I^A$ (Group A), $I^A I^B$ (Group AB).
- If mother is $I^A i$: $I^A I^A$ (Group A), $I^A I^B$ (Group AB), $I^A i$ (Group A), $I^B i$ (Group B).
- Therefore, children can be Blood Group **A**, **B**, or **AB**. Blood Group **O ($ii$) is IMPOSSIBLE** because the father ($I^A I^B$) always donates either $I^A$ or $I^B$.
- **Rh System**:
- Mother is $\text{Rh}^+$ ($RR$ or $Rr$) and father is $\text{Rh}^+$ ($RR$ or $Rr$).
- If both are heterozygous ($Rr$), an $\text{Rh}^-$ ($rr$) child is genetically possible.
**2. Option Analysis**:
- **Option (A) [Blood group A+] is CORRECT**: Possible genotype $I^A I^A$ or $I^A i$ with $\text{Rh}^+$.
- **Option (B) [Blood group O+] is INCORRECT**: An AB father cannot produce an O child ($ii$).
- **Option (C) [Blood group B+] is CORRECT**: Possible when mother contributes allele $i$ and father contributes $I^B$ ($I^B i$).
- **Option (D) [Blood group O-] is INCORRECT**: Allele $i$ from father is impossible.
**3. Final Answer**:
- **Correct Options**: **A, C**
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