A and B are friends. They decide to meet between 1:00 pm and 2:00 pm on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is: A. 1/4 B. 1/16 C. 7/16 D. 9/16

GATE 2012 · General Aptitude · Probability · medium

Answer: P(A and B meet) = 7/16. Answer: C. 7/16

1. Set up the sample space: Total area = 60 * 60 = 3600 square minutes
2. Identify the unfavorable region: Two right triangles, each with legs = 60 - 15 = 45. Area of each = (45^2)/2 = 1012.5. Total unfavorable = 2 * 1012.5 = 2025
3. Compute the probability of meeting: P(meet) = (3600 - 2025) / 3600 = 1575/3600 = 7/16 = 0.4375