Question

Suppose that in a certain shop, there is a little (sort of) traffic light in the counter. When finishing their purchase, the buyer has to activate a button which makes the light go either green or red. If the light goes green, the client gets their purchase for free. The light is programmed to go green with a probability of 0.015.

a) Calculate the probability that the fiftieth customer who activates the button will be the first to take their free purchase.
b) Determine the average number of times the traffic light must be operated so that the green light comes on for the first time.
c) Calculate the probability that the hundredth customer that activates the button will be the second to take their free purchase.

Answer 1

solution: p=0.015 & q= 1-p=0.985 15-1 <a) Xn Geomelic distribution P(x=15) = x ' p = (0.985) 16.015) = 10:0121 (b) f(x) 1. dois = 66.67 0.015 60 y Negative kimonial P(x=100) - let') coobs" (0.3892 10o-2 00-1 2 - 1 = 10.oosi