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Arrivals at a telephone booth are considered to be poisson with an average time of 10 minutes between one arrival and the next. The length of a phone call is assumed to be distributed exponentially with mean of 3 minutes. The probability that a person arriving at the hook will have to wait, is:
A)0.043
B)0.300
C)0.429
D)0.700
Correct Answer:
D
Solution :
\[\rho =\frac{\lambda }{\mu }=\frac{3}{10}=0.3\] Probability of waiting \[=1-\rho =1-0.3=0.7\]