55. A heterozygous tall plant (Tt) was crossed with a homozygous dwarf plant (tt).
The resultant seeds were collected. If five seeds are chosen at random, then the
probability (in %) that exactly two of these seeds will yield dwarf plants is
__________.
Probability Exactly 2 Dwarf Plants from Tt × tt Cross
Monohybrid Test Cross Analysis
Heterozygous tall plant (Tt) produces gametes T and t equally (50% each). Homozygous dwarf (tt) produces only t gametes. This test cross yields 50% Tt (tall) and 50% tt (dwarf) offspring with 1:1 phenotypic ratio.
Punnett Square:
Tt × tt → 50% dwarf probability per seed (p = 0.5)
Tt × tt → 50% dwarf probability per seed (p = 0.5)
Binomial Probability Formula
For exactly 2 dwarf plants in 5 seeds, use binomial probability:
P(k=2) = C(5,2) × (0.5)2 × (0.5)3 = 10 × 0.03125 = 0.3125 (31%)
Step-by-Step Calculation
- n = 5 seeds, k = 2 dwarfs, p = 0.5 (dwarf probability)
- Combinations: C(5,2) = 5!/(2!×3!) = 10
- Probability: 10 × (0.5)5 = 10 × 0.03125 = 0.3125
- Convert to percentage: 31.25% ≈ 31%
Correct Answer: 31%
Options Analysis Table
| Option | Calculation | Why Correct/Incorrect |
|---|---|---|
| 20% | C(5,2)×(0.4)²×(0.6)³ ≈ 0.2 | ❌ Wrong p=0.4; test cross is 1:1 (p=0.5), not 3:1 |
| 25% | (0.5)² = 0.25 | ❌ Single seed probability, ignores binomial distribution |
| 31% | C(5,2)×(0.5)⁵ = 0.3125 | ✅ Exact binomial calculation |
| 50% | Overall dwarf proportion | ❌ For single seed, not “exactly two” in five seeds |
Key SEO Phrases
- Primary: probability exactly two dwarf plants five seeds Tt tt cross
- Secondary: genetics binomial probability NEET, test cross probability calculation
- Long-tail: heterozygous tall plant crossed homozygous dwarf five seeds exactly two dwarf
