Hurry Yan Yau!!!

Discrete Mathematics Level 5

Yan Yau is going to school. There are 2 different buses that Yan Yau could take: the C4 and the C9 bus. They both leave at the plaza and have different schedules. The C4 bus takes 9 minutes and the C9 bus takes 4 minutes to reach to the school. Here is a portion of the schedule for the C4 bus: \(10:10,10:16,10:28,10:40,10:46,10:58,11:10\)

Here is a portion of the schedule for the C9 bus: \(10:04,10:10,10:22,10:34,10:40,10:52,11:04\)

Yan Yau arrives at the bus stop at a random time at the bus stop between 10:00 and 11:00. He will take the first bus that leaves;if both leave at the same time, then he will choose the bus that takes the least time to get to school.The probability that Yan Yau takes the C9 bus can be expressed as \(\frac{a}{b}\) where \( a\) and \(b\) are positive coprime integers.

Also, what is the expected number of minutes after 10:00 when Yan Yau arrives at the school?Round off your answer to the nearest integer and let it be \(c\).

Ultimately, find the value of \(a+b+c\).


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