18. If Janine obeys all traffic laws, what is the probability, to the nearest percent, that Janine will stop only at Intersections B and C and not at Intersections A and D on her way to work on any given day?
Answer: B
Janine has a 4% probability of stopping only at Intersections B and C and not at Intersections A and D.
To calculate the probability that Janine stops only at Intersections B and C while not stopping at Intersections A and D, we multiply the stopping probabilities for B and C and the non-stopping probabilities for A and D. The result yields a probability of approximately 4%.
A) 2%
This option is incorrect as it underestimates the combined probabilities. The calculations show that the probability of stopping at B and C while not stopping at A and D is higher than 2%.
B) 4%
This option is correct because the calculated probability of Janine stopping at Intersections B and C (each with a certain percentage) and not stopping at Intersections A and D yields a total of 4%. This directly aligns with the requirements of the question.
C) 12%
This option is incorrect as it overestimates the probability. The calculations indicate that the combined probabilities of stopping at B and C and not at A and D result in a lower percentage than 12%.
D) 42%
This option is incorrect because it significantly overestimates the probability. The calculated probabilities do not support a total of 42% for the specific stopping conditions outlined in the question.
E) 70%
This option is incorrect as it greatly exceeds the calculated probability. The calculations clearly do not support the notion that Janine would have a 70% chance of stopping only at Intersections B and C.
Conclusion
The correct answer of 4% accurately reflects the specific conditions under which Janine stops at the intersections. All other options fail to align with the calculated probabilities, making them invalid choices. Understanding the independent probabilities of each intersection is crucial for solving this problem correctly.