Question

The probability of a customer arrival at a grocery service counter in any 1 second is equal to 0,1. Assume that customers arrive in a random stream and hence that the arrival any 1 second is independent of any other. Calculate the probability that the first arrival will occur during the third   1-second interval.

Answer 1

$p=0.1 \\ q=1-q=0.9$

Geometric probability:

$p(y) = q^{y-1}p \\ p(3) = 0.9^{3-1} \times 0.1 = 0.081 = 8.1 \;\%$