A certain bus arrives at the bus stop near Duru's house with probability $\dfrac{7}{10}$ at exactly 09:02 and with probability $\dfrac{3}{10}$ at exactly 09:03. Duru leaves home at exactly 09:00 to catch this bus. The time it takes for Duru to reach the stop is 100 seconds with probability $\dfrac{1}{2}$, 150 seconds with probability $\dfrac{3}{10}$, and 250 seconds with probability $\dfrac{1}{5}$. What is the probability that Duru is at the stop when the bus arrives? A) $\dfrac{55}{100}$ B) $\dfrac{59}{100}$ C) $\dfrac{63}{100}$ D) $\dfrac{67}{100}$ E) $\dfrac{71}{100}$
A certain bus arrives at the bus stop near Duru's house with probability $\dfrac{7}{10}$ at exactly 09:02 and with probability $\dfrac{3}{10}$ at exactly 09:03. Duru leaves home at exactly 09:00 to catch this bus. The time it takes for Duru to reach the stop is 100 seconds with probability $\dfrac{1}{2}$, 150 seconds with probability $\dfrac{3}{10}$, and 250 seconds with probability $\dfrac{1}{5}$.
What is the probability that Duru is at the stop when the bus arrives?
A) $\dfrac{55}{100}$
B) $\dfrac{59}{100}$
C) $\dfrac{63}{100}$
D) $\dfrac{67}{100}$
E) $\dfrac{71}{100}$