Let's solve this step by step.
Given:
- The allele for tall plants (T) is dominant over the allele for short plants (t).
- The allele for purple flowers (P) is dominant over the allele for white flowers (p).
- Two plants that are heterozygous for both traits (TtPp) are crossed.
We need to determine the probability of an offspring being short (tt) and having white flowers (pp).
We break the problem down:
1. Genotype Probability for Height (short = tt):
- Each parent is Tt.
- Probability of getting t from one parent = [tex]\( \frac{1}{2} \)[/tex]
- Probability of getting t from the other parent = [tex]\( \frac{1}{2} \)[/tex]
- Therefore, the probability of offspring being tt (short) is [tex]\( \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \)[/tex]
2. Genotype Probability for Flower Color (white = pp):
- Each parent is Pp.
- Probability of getting p from one parent = [tex]\( \frac{1}{2} \)[/tex]
- Probability of getting p from the other parent = [tex]\( \frac{1}{2} \)[/tex]
- Therefore, the probability of offspring being pp (white) is [tex]\( \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \)[/tex]
3. Combined Probability for Both Traits (short and white):
- The events are independent, so we multiply the probabilities.
- Probability of ttpp = Probability of tt [tex]\( \times \)[/tex] Probability of pp
- Therefore, the combined probability is [tex]\( \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \)[/tex]
Thus, the probability of an offspring being short and having white flowers is [tex]\( \frac{1}{16} \)[/tex].
Therefore, the answer is [tex]\( \boxed{\frac{1}{16}} \)[/tex].
