JOMO 7, Short 6

Probability Level 4

Yan Yau is going to school. There are 2 different buses that Yan Yau could take: the C4 and the C9. They both leave at the plaza and have different schedules. The C4 bus takes $9$ minutes to get to school and the C9 takes $4$ minutes.

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 between 10:00 and 11:00. He will take the first bus that leaves; if both buses depart at the same time, then he will choose the bus that takes the least time for him 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. Find the value of $a+b$ .

The answer is 8.

2 solutions

Aaron Paul
Sep 13, 2014

c9 bus could be caught by our hero for 36 min b/w 10 am to 11 am so probability for c9 bus is 36/60=3/5=a/b so we are with a+b=eight(8)

James Pohadi
Jan 4, 2017

Yan Yau will take $C9$ bus if he arrives between:

$\begin{aligned} * 10:00-10:10 &\implies 10 \text{ minutes} \\ *10:16-10:22 &\implies 6 \text{ minutes} \\ * 10:28-10:40 &\implies 12 \text{ minutes} \\ * 10:46-10:52 &\implies 6 \text{ minutes} \\ * 10:58-11:00 &\implies 2 \text{ minutes} \\ total &\implies 36 \text{ minutes} \end{aligned}$

$P=\dfrac{36}{60}=\dfrac{3}{5}$

$a=3$ , $b=5$ . $a+b=3+5=\boxed{8}$

JOMO 7, Short 6

The answer is 8.

2 solutions

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