To find \( P(A \text{ and } B) \) for two independent events, you can use the formula:
\[ P(A \text{ and } B) = P(A) \times P(B) \]
Given \( P(A) = 47 \) and \( P(B) = 67 \), you would multiply these to find \( P(A \text{ and } B) \):
\[ P(A \text{ and } B) = 47 \times 67 \]
Now, calculating that:
\[ 47 \times 67 = 3149 \]
However, this value seems impractical because probabilities should range between 0 and 1 (or often expressed as fractions or decimals). It’s possible that the values you've provided for \( P(A) \) and \( P(B) \) are not traditional probabilities but rather scaled values.
If \( P(A) \) and \( P(B) \) are meant to represent percentages or a similar scale, you would need to convert them to probabilities first (for example, if they refer to 47% and 67%).
So, first, convert them:
\[ P(A) = 0.47 \quad \text{and} \quad P(B) = 0.67 \]
Then, multiply:
\[ P(A \text{ and } B) = 0.47 \times 0.67 \]
Calculating gives:
\[ 0.47 \times 0.67 = 0.3149 \]
This doesn't correspond to any of your answer choices either.
Please check to ensure \( P(A) \) and \( P(B) \) are expressed correctly, or if they should be percentages or another type of scale. The raw multiplication does not yield a value easily comparable to the answer choices provided.