Final answer:
To find the probability that a and b meet each other, we need to consider the overlapping time intervals between their arrivals. The probability can be calculated by dividing the range of meeting time intervals by the total time interval.
Step-by-step explanation:
To find the probability that a and b meet each other, we need to consider the overlapping time intervals between their arrivals. Let's break down the problem step by step:
1. Find the total time interval in which a and b can arrive. In this case, it is from 12:00 to 14:00, which is 120 minutes.
2. Determine the range of time intervals in which a and b can meet. Since a stays for 20 minutes and b stays for 10 minutes, the range of meeting time intervals is from the start time of a's arrival to the end time of b's stay, which is from 12:00 to 13:10.
3. Calculate the probability of meeting by dividing the range of meeting time intervals by the total time interval. In this case, the range of meeting time intervals is 70 minutes (13:10 - 12:00), so the probability of meeting is 70/120 = 7/12 or approximately 0.5833.
Therefore, the probability that a and b meet each other is approximately 0.5833.