Let's denote the events as follows:
- \( A \): The event that a driver stops at every red light.
- \( B \): The event that a driver stops completely at every stop sign.
From the information provided in the problem:
- \( P(A) = 0.98 \) (98% of drivers stop at every red light).
- \( P(A \cap B) = 0.77 \), which means the probability that a driver both stops at every red light and stops completely at every stop sign is 77% of drivers.
Now we want to find the conditional probability \( P(B | A) \), which is the probability that a driver stops completely at every stop sign given that they stop at every red light. We can use the definition of conditional probability:
\[ P(B | A) = \frac{P(A \cap B)}{P(A)} \]
Substituting the known values into the formula, we find:
\[ P(B | A) = \frac{0.77}{0.98} \]
Now, let's perform the calculation:
\[ P(B | A) = \frac{0.77}{0.98} \approx 0.7857142857 \]
To convert this to a percentage, we multiply by 100:
\[ P(B | A) \approx 78.57% \]
Rounding to the nearest whole percent, we get:
\[ P(B | A) \approx 79% \]
Thus, the probability that a driver stops completely at every stop sign, given that they stop at every red light, is approximately \( 79% \).