Answer: The expected waiting time is [tex]1\dfrac{2}{3}\ min[/tex]
Step-by-step explanation:
Since we have given that
Average waiting time for slow elevator = 3 min
Average waiting time for fast elevator = 1 min
probability that a person choose the fast elevator = [tex]\dfrac{2}{3}[/tex]
Probability that a person choose the slow elevator = [tex]\dfrac{1}{3}[/tex]
So, the expected waiting time would be
[tex]E[x]=\sum xp(x)=3\times \dfrac{1}{3}+1\times \dfrac{2}{3}\\\\=1+\dfrac{2}{3}\\\\=\dfrac{3+2}{3}\\\\=\dfrac{5}{3}\\\\=1\dfrac{2}{3}\ min[/tex]
Hence, the expected waiting time is [tex]1\dfrac{2}{3}\ min[/tex]
