Simplify:   ($\left(2\frac{1}{4}+\mathrm{3.8\; )}\right)-2\frac{1}{5}$

The correct option is 3.85.

To simplify the given numerical expression, we follow the standard order of operations (BODMAS/PEMDAS), which requires us to perform operations inside the parentheses first.

The given expression is:

$\left(2\frac{1}{4}+3.8\right)-2\frac{1}{5}$

Step 1: Convert all mixed numbers to decimals for ease of calculation.

First, convert the mixed fraction $2\frac{1}{4}$:

$2\frac{1}{4}=2+\frac{1}{4}=2+0.25=2.25$

Next, convert the mixed fraction $2\frac{1}{5}$:

$2\frac{1}{5}=2+\frac{1}{5}=2+0.2=2.2$

Step 2: Substitute the decimal values back into the expression.

The expression becomes:

$\left(2.25+3.8\right)-2.2$

Step 3: Perform addition inside the parentheses.

$2.25+3.8=6.05$

Step 4: Subtract $2.2$ from $6.05$.

$6.05-2.2=3.85$

Thus, the simplified result is 3.85.