In a DNA fragment of 10kbp, (10000base pairs ) how many recongnition sites of EcoRl are theoretically possible ?

Options

A. 3
B. 5
C. 30
D. 2

Answer

To determine how many recognition sites of EcoRI are theoretically possible in a DNA fragment of 10 kbp (10,000 base pairs), we can follow these steps:

### Step 1: Identify the recognition sequence of EcoRI
EcoRI recognizes the specific DNA sequence: **GAATTC**. This sequence consists of **6 base pairs**.

### Step 2: Calculate the probability of the recognition site occurring
To find out how many times this recognition site can theoretically occur in a DNA fragment, we first need to calculate the probability of the sequence GAATTC appearing.

Since there are 4 different nucleotides (A, T, C, G), the probability of any specific base appearing at a given position is 1/4. Therefore, for a sequence of 6 bases, the probability of the entire sequence GAATTC occurring is:

\[ P(GAATTC) = \left(\frac{1}{4}\right)^6 = \frac{1}{4096} \]

### Step 3: Determine the number of possible sites in 10,000 base pairs
Now, we need to calculate how many times we can expect this sequence to appear in a DNA fragment of 10,000 base pairs.

To find the expected number of occurrences, we can use the formula:

\[ \text{Expected occurrences} = \text{Total base pairs} \times P(GAATTC) \]

Substituting the values:

\[ \text{Expected occurrences} = 10,000 \times \frac{1}{4096} \]

### Step 4: Calculate the expected occurrences
Now, we perform the calculation:

\[ \text{Expected occurrences} = \frac{10,000}{4096} \approx 2.44 \]

Since we cannot have a fraction of a recognition site, we round this down to the nearest whole number, which gives us **2**.

### Conclusion
Thus, the theoretical number of recognition sites of EcoRI in a DNA fragment of 10 kbp is **2**.

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