Geometric Probability
Two friends agree to meet between five and six o'clock, each arriving at a uniformly random time and waiting fifteen minutes for the other; what is the probability that the two friends actually meet?
Select the correct option:
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More statistics and probability Practice Questions
A group of ten numbers has a recorded mean of fifteen, but later one entry originally read as eight ...
A group of ten numbers has a recorded mean of fifteen, but later one entry originally read as eight ...
A binomial random variable representing successes in n trials has mean equal to 4 and variance equal...
A binomial random variable representing successes in n trials has mean equal to 4 and variance equal...
From a committee containing seven men and five women, a subcommittee of three persons is selected at...
From a committee containing seven men and five women, a subcommittee of three persons is selected at...
An urn holds four red and six blue balls, and one ball drawn at the first stage is set aside without...
An urn holds four red and six blue balls, and one ball drawn at the first stage is set aside without...
When every observation in a dataset is first multiplied by three and then increased by five, how doe...
When every observation in a dataset is first multiplied by three and then increased by five, how doe...
Suppose events A and B satisfy P(A) = 1/2, P(B) = 1/3, and the conditional probability P(A given B) ...
Suppose events A and B satisfy P(A) = 1/2, P(B) = 1/3, and the conditional probability P(A given B) ...
A diagnostic test detects a disease present in one percent of a population with sensitivity ninety-n...
A diagnostic test detects a disease present in one percent of a population with sensitivity ninety-n...
In a binomial setting where a marksman hits a target with probability 1/4 on each independent shot, ...
In a binomial setting where a marksman hits a target with probability 1/4 on each independent shot, ...
Two distinct groups contain twenty and thirty students with mean marks of sixty and seventy respecti...
Two distinct groups contain twenty and thirty students with mean marks of sixty and seventy respecti...
Two players alternately roll a fair die starting with the first player, and whoever first rolls a si...
Two players alternately roll a fair die starting with the first player, and whoever first rolls a si...
A fair six-faced die is rolled once and the random variable X equals the number shown on the top fac...
A fair six-faced die is rolled once and the random variable X equals the number shown on the top fac...
Given two events with P(A) = 0.6 and P(B) = 0.5 inside a sample space, while their union has probabi...
Given two events with P(A) = 0.6 and P(B) = 0.5 inside a sample space, while their union has probabi...
About This Question
- Subject
- mathematics
- Chapter
- statistics and probability
- Topic
- geometric probability
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
7/16
Geometric probability replaces counting with measuring areas when outcomes are continuous and uniformly distributed, so probability equals favourable area divided by total area. This area-based modelling is a hallmark of harder JEE Advanced probability. Let the two arrival times x and y, in minutes after five o'clock, range over the 60 × 60 square of area 3600. The friends meet when their arrival times differ by at most 15 minutes, that is |x − y| ≤ 15. The non-meeting region consists of two right triangles where |x − y| > 15, each with legs of length 60 − 15 = 45, so each triangle has area (1/2)(45)(45) = 1012.5, totalling 2025. The favourable meeting area is 3600 − 2025 = 1575, giving probability 1575/3600 = 7/16. Option 1/4 wrongly squares the single ratio 15/60. Option 9/16 reports the complement, the non-meeting probability. Option 1/2 ignores the geometry entirely. The method uses the uniform-area definition of probability over the square sample space. Plausibility check: 7/16 ≈ 0.44 is below one-half, sensible because a 15-minute window within a 60-minute interval gives less than even odds of overlap.
This hard difficulty mathematics question is from the chapter statistics and probability, covering the topic of geometric probability. It appeared in the 2025 exam.
Looking for more practice? Explore all mathematics questions or browse statistics and probability questions on RankGuru.