Q.65 Two true–breeding snapdragon (Antirrhinum majus) plants, one with red flowers and
another with white flowers were crossed. The F1 plants were all with pink flowers. When
the F1 plants were selfed, they produced three kinds of F2 plants with red, pink and white
flowers in a 1:2:1 ratio. The probability that out of the five plants picked up randomly, two
would be with pink flowers, two with white flowers and one with red flowers is _____%.
Snapdragon flower color inheritance follows incomplete dominance, producing a
1 red : 2 pink : 1 white phenotypic ratio in the F2 generation.
This corresponds to probabilities of 1/4 red, 1/2 pink,
and 1/4 white. Using the multinomial formula, we can calculate the probability
of obtaining exactly 1 red, 2 pink, and 2 white plants out of 5 randomly selected F2 plants.
Genetic Cross Details
A true-breeding red snapdragon (RR) crossed with a true-breeding white snapdragon
(rr) produces all pink F1 plants (Rr).
This confirms incomplete dominance, where heterozygotes show an intermediate phenotype.
Selfing the F1 generation (Rr × Rr) gives the following Punnett square:
| R | r | |
|---|---|---|
| R | RR (red) | Rr (pink) |
| r | Rr (pink) | rr (white) |
Thus, the F2 phenotypic ratio is:
- Red (RR): 1/4
- Pink (Rr): 1/2
- White (rr): 1/4
Probability Calculation
This is a multinomial distribution problem with:
- P(red) = 1/4
- P(pink) = 1/2
- P(white) = 1/4
- Total plants (n) = 5
The probability of exactly 1 red, 2 pink, and 2 white plants is:
5! / (1! × 2! × 2!) × (1/4)1 × (1/2)2 × (1/4)2
= 30 × (1/4) × (1/4) × (1/16)
= 30 / 1024
= 0.0293
As a percentage, the probability is 2.93%.
Key Genetics Insight
- Incomplete dominance causes heterozygotes (Rr) to appear pink.
- Selfing pink F1 plants produces a 1:2:1 red:pink:white ratio in F2.
Step-by-Step Summary
- F2 probabilities: Red = 0.25, Pink = 0.5, White = 0.25
- Multinomial coefficient: 5! / (1!2!2!) = 30
- Final probability: 30 × (0.25)1 × (0.5)2 × (0.25)2 = 0.0293
This calculation is directly applicable to CSIR NET–level genetics problems
involving snapdragon flower color inheritance and probability.
