What is the probability of gamete AbC produced by a plant having genotype AaBbCc (If all the genes are situated on different chromosomes) ?

Options

A. `(1)/(2)`
B. `(1)/(4)`
C. `(1)/(6)`
D. `(1)/(8)`

Answer

To determine the probability of producing the gamete AbC from a plant with the genotype AaBbCc, we can follow these steps:

### Step 1: Identify the alleles for each gene
The genotype of the plant is AaBbCc. This means:
- For gene A, the alleles are A (dominant) and a (recessive).
- For gene B, the alleles are B (dominant) and b (recessive).
- For gene C, the alleles are C (dominant) and c (recessive).

### Step 2: Determine the possible gametes
Since the genes are on different chromosomes, they assort independently. Each gene can contribute one of its two alleles to the gamete.

- For gene A (Aa), the possible alleles are A or a.
- For gene B (Bb), the possible alleles are B or b.
- For gene C (Cc), the possible alleles are C or c.

### Step 3: Calculate the probability of each allele in the gamete AbC
To form the gamete AbC, we need:
- A from gene A (probability = 1/2)
- b from gene B (probability = 1/2)
- C from gene C (probability = 1/2)

### Step 4: Multiply the probabilities
Since the alleles assort independently, we multiply the probabilities of each allele:
\[ \text{Probability of gamete AbC} = P(A) \times P(b) \times P(C) \]
\[ = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \]
\[ = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8} \]

### Conclusion
The probability of producing the gamete AbC from the plant with genotype AaBbCc is \( \frac{1}{8} \).

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