GATE 2019 BT Q.47: solution and answer

Official answer: 0.75Source: Official answer key, GATE 2019 BT (IIT Madras)

1. Purple is the dominant phenotype (allele $P$) and white is recessive (allele $p$); an offspring with white flowers must be homozygous recessive, genotype $pp$.

2. Both parents show the purple (dominant) phenotype, yet one of their offspring is $pp$. Since a $pp$ offspring must receive a recessive allele from each parent, neither parent can be homozygous dominant $PP$ (a $PP$ parent could never contribute a $p$ allele). Hence both purple-flowered parents must be heterozygous: $Pp\times Pp$.

3. A monohybrid cross $Pp\times Pp$ gives the genotypic ratio $1PP:2Pp:1pp$, i.e. a phenotypic ratio of $3$ purple $:1$ white. So for any single offspring of this cross, $P(\text{purple})=\frac{3}{4}$ and $P(\text{white})=\frac{1}{4}$.

4. Each offspring arises from an independent fertilization event, so the phenotype of one offspring (here, the first offspring being white) gives no information about, and does not change, the probability distribution for any other offspring, including the third.

5. Therefore the probability that the third offspring has purple flowers is $$P(\text{purple})=\frac{3}{4}=0.75$$