As per probability , the frequency of occurrene the paindormic sequence recognized by Eco Rl is (Assuming that the occurrence of bases in adjacent positions is random on DNA)

Options

A. once in 9046 nucleotides
B. once in 4069 nucleotides
C. once in 4096 nucleotides
D. once in 6096 nucleotides

Answer

To find the frequency of occurrence of the palindromic sequence recognized by EcoRI (GAA TTC), we will use probability principles. Here’s a step-by-step breakdown of the solution:

### Step-by-Step Solution:

1. **Identify the Sequence**: The recognition site of EcoRI is GAA TTC. This sequence consists of 6 nucleotides.

2. **Understand the Probability of Each Nucleotide**: In DNA, there are four types of nucleotide bases: Adenine (A), Thymine (T), Cytosine (C), and Guanine (G). Assuming the bases occur randomly, the probability of each base appearing at any given position is:
- P(A) = 1/4
- P(T) = 1/4
- P(C) = 1/4
- P(G) = 1/4

3. **Calculate the Probability of the Entire Sequence**: Since the bases are independent, the probability of the entire sequence (GAA TTC) occurring can be calculated by multiplying the probabilities of each individual base:
- P(G) = 1/4
- P(A) = 1/4
- P(A) = 1/4
- P(T) = 1/4
- P(T) = 1/4
- P(C) = 1/4

Therefore, the probability of the sequence GAA TTC is:
\[ P(GAA TTC) = P(G) \times P(A) \times P(A) \times P(T) \times P(T) \times P(C) = \left(\frac{1}{4}\right)^6 \]

4. **Calculate the Value**:
\[ P(GAA TTC) = \frac{1}{4^6} = \frac{1}{4096} \]

5. **Interpret the Result**: This probability means that the sequence GAA TTC is expected to occur once in every 4096 nucleotide bases in a random DNA sequence.

### Final Answer:
The frequency of occurrence of the palindromic sequence recognized by EcoRI is **1 in 4096 nucleotides**.