Question
98% of drivers stop at every red light. Some percentage of those that stop at every red light also stop completely at every stop sign. There is a 77% probability that a driver stops at a red light and stops completely at stop signs. Given that a driver stops at every red light, what is the probability that they also stop completely at every stop sign, rounded to the nearest whole percent?
Answers
GPT-4o mini
To solve this problem, we can use the principles of conditional probability.
Based on the information provided:
- Let \( R \) be the event that a driver stops at every red light.
- Let \( S \) be the event that a driver stops completely at every stop sign.
From the problem, we are given that:
- \( P(R) = 0.98 \) (98% of drivers stop at every red light)
- \( P(S | R) = 0.77 \) (the probability that a driver stops completely at every stop sign, given that they stop at every red light, is 77%).
We are asked for \( P(S | R) \), which is already given as 0.77.
To express this in percentage, we multiply by 100:
\[
P(S | R) = 0.77 \times 100 = 77\%
\]
Therefore, the probability that a driver stops completely at every stop sign, given that they stop at every red light, is \( \boxed{77} \) percent.
Based on the information provided:
- Let \( R \) be the event that a driver stops at every red light.
- Let \( S \) be the event that a driver stops completely at every stop sign.
From the problem, we are given that:
- \( P(R) = 0.98 \) (98% of drivers stop at every red light)
- \( P(S | R) = 0.77 \) (the probability that a driver stops completely at every stop sign, given that they stop at every red light, is 77%).
We are asked for \( P(S | R) \), which is already given as 0.77.
To express this in percentage, we multiply by 100:
\[
P(S | R) = 0.77 \times 100 = 77\%
\]
Therefore, the probability that a driver stops completely at every stop sign, given that they stop at every red light, is \( \boxed{77} \) percent.