Question

A cable provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the new digital TV service the company has provided. All numbers are in the 590 ​exchange, so there are 10 comma 000 possible numbers from 590​-0000 to 590​-9999. If they select the numbers with equal​ probability: ​a) What distribution would they use to model the​ selection? ​b) What is the probability the number selected will be an odd ​number? ​c) What is the probability the number selected will end in 999​?

Answer 1

a) Discrete Uniform Distribution

b) 0.5

c) 0.001

Explanation:

a) What distribution would they use to model the selection?

Since each number has equal probability of being selected, they would be using a Discrete Uniform Distribution.

b) What is the probability the number selected will be an odd number?

Since there are 5,000 odd numbers between 0 and 9999

P(odd)=5,000/10,000 = ½ = 0.5

c) What is the probability the number selected will end in 999?

There are only 10 numbers ending in 999:

0999, 1999, 2999,...,9999

hence

P(number ends in 999)=10/10,000 = 1/1,000 = 0.001