A meeting occurs if the person arrives between 1:00 PM and 1:45 PM and the second person arrives in the next 15 minutes or if both the persons arrive between 1:45 and 2:00. Case 1: 45/60 are favorable cases and hence the probability of first-person arriving between 1:00 and 1:45 is 3/4. Probability of second person arriving in the next 15 min = 15/60 = 1/4 So, the probability of one person arriving between 1:00 and 1:45 and meeting the other = 3/4 × 1/4 × 2 = 3/8 (2 for choosing the first arriving friend) Case 2: Both friends must arrive between 1:45 and 2:00 Probability = 1/4 × 1/4 = 1/16 So, probability of a meet = 3/8 + 1/16 = 7/16 Hence, the correct answer is 7/16.