In the given model \( y = 1 + 0.02x \), \( y \) represents the estimated number of fraudulent charges, and \( x \) represents the total number of credit card charges.
Here, we need to estimate the number of fraudulent charges out of \( 200 \) total charges. We can substitute \( x = 200 \) into the model:
\[ y = 1 + 0.02 \cdot 200 \]
Calculating the term \( 0.02 \cdot 200 \):
\[ 0.02 \cdot 200 = 4 \]
Now we can substitute this back into the equation:
\[ y = 1 + 4 = 5 \]
Therefore, the estimated number of fraudulent credit card charges out of 200 charges is \( 5 \).