Questions: If a plant heterozyous for three genes (DdEeff) is allowed to self-pollinate, what is the probability that the offspring will be homozygous recessive for all three genes? 1/64 1/16 1 / 32 1 / 4 1/12

To determine the probability that the offspring will be homozygous recessive for all three genes (dd ee ff) when a plant heterozygous for three genes (DdEeff) is allowed to self-pollinate, we need to consider each gene pair separately and then multiply the probabilities.

1. Gene Dd:

   • The possible genotypes from self-pollination of Dd are DD, Dd, and dd.
   • The probability of being homozygous recessive (dd) is 1/4.

2. Gene Ee:

   • The possible genotypes from self-pollination of Ee are EE, Ee, and ee.
   • The probability of being homozygous recessive (ee) is 1/4.

3. Gene ff:

   • Since the plant is homozygous recessive for this gene (ff), all offspring will be ff.
   • The probability of being homozygous recessive (ff) is 1.

Now, we multiply the probabilities for each gene to find the overall probability of being homozygous recessive for all three genes:

\[ \text{Probability} = \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) \times 1 = \frac{1}{16} \]

Therefore, the probability that the offspring will be homozygous recessive for all three genes is \(\frac{1}{16}\).

Explanation of Options:

• 1/64: Incorrect. This would be the probability if all three genes were heterozygous and the probability for each was 1/4.
• 1/16: Correct. This is the calculated probability considering the given genotypes.
• 1/32: Incorrect. This does not match the calculated probability.
• 1/4: Incorrect. This would be the probability if only one gene was considered.
• 1/12: Incorrect. This does not match the calculated probability.

In summary, the answer is 1/16.