Question

In a diploid angiosperm species, flower colour is regulated by the R gene. RR and Rr genotypes produce red flowers, whereas the rr genotype produces white flowers. If two individual plants are randomly selected from a large segregating population of a genetic cross between RR and rr parents, the probability of both the plants producing red flowers is _______. (Rounded off to two decimal places)

Hint:

For independent random selections, multiply individual probabilities. Here, since red occurs with $3/4$ frequency, the probability for two independent choices is $(3/4)^2$.

Answer 1

Step 1: Parent cross. Cross between $RR \times rr ⇒$ F$_1$ = 100% $Rr$ (red).
Step 2: F$_2$ population. Selfing of $Rr \times Rr ⇒$ Genotypic ratio: $1RR:2Rr:1rr$.
Phenotypic ratio: $3$ red ($RR$ + $Rr$) : $1$ white ($rr$).
Step 3: Probability of red. $P(\text{red}) = \tfrac{3}{4} = 0.75$.
Step 4: Probability that both chosen are red. \[ P(\text{both red}) = 0.75 \times 0.75 = 0.5625 \approx 0.56. \]