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The probability of a customer arrival at a grocery service
Chapter 3, Problem 75E(choose chapter or problem)
Problem 75E
The probability of a customer arrival at a grocery service counter in any one second is equal to .1. Assume that customers arrive in a random stream and hence that an arrival in any one second is independent of all others. Find the probability that the first arrival
a will occur during the third one-second interval.
b will not occur until at least the third one-second interval.
Questions & Answers
QUESTION:
Problem 75E
The probability of a customer arrival at a grocery service counter in any one second is equal to .1. Assume that customers arrive in a random stream and hence that an arrival in any one second is independent of all others. Find the probability that the first arrival
a will occur during the third one-second interval.
b will not occur until at least the third one-second interval.
ANSWER:
Solution 75E
Step1 of 3:
Let us consider random variable ‘X’ it presents the customer arrival at a grocery service counter in any one second. Assume that customers arrive in a random stream and hence that an arrival in any one second is independent of all others. And we have p = 0.1.
That is XGeometric(p)
XGeometric(
)
Here our goal is:
a). We need to find the probability of will occur during the third one-second interval.
b). We need to find the probability of will not occur until at least the third one-second interval.
Step2 of 3:
a).
Then the probability mass function of geometric distribution is given by: