GATE CE 2025 Set 1 — Question 63
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Engineering Mathematics → Probability → PMF, PDF & CDF
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Question
A one-way, single lane road has traffic that consists of 30% trucks and 70% cars. The speed of trucks (in km/h) is a uniform random variable on the interval (30, 60), and the speed of cars (in km/h) is a uniform random variable on the interval (40, 80). The speed limit on the road is 50 km/h. The percentage of vehicles that exceed the speed limit is __________________ (rounded off to 1 decimal place).Note: is a uniform random variable on the interval , if its probability density function is given by
Correct answer
61 to 63
Solution
Given:
,
Speed of trucks,
Speed of cars,
Speed limit, Step 1: Calculate the probability that a truck exceeds the speed limit.
Step 2: Calculate the probability that a car exceeds the speed limit.
Step 3: Calculate the total probability of a vehicle exceeding the speed limit using the Law of Total Probability.
Step 4: Convert to percentage.
Percentage .
,
Speed of trucks,
Speed of cars,
Speed limit, Step 1: Calculate the probability that a truck exceeds the speed limit.
Step 2: Calculate the probability that a car exceeds the speed limit.
Step 3: Calculate the total probability of a vehicle exceeding the speed limit using the Law of Total Probability.
Step 4: Convert to percentage.
Percentage .
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