SOLUTION: an integer from 100 through 999 inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least 1 digit? my act answer key got d but i

Algebra ->  Probability-and-statistics -> SOLUTION: an integer from 100 through 999 inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least 1 digit? my act answer key got d but i       Log On


   

Question 550033: an integer from 100 through 999 inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least 1 digit? my act answer key got d but i don't know how so i could please explain it to me with work, then that would be great. Help is much appreciated, have a great day!
a.19/900
b.81/100
c.90/900
d.171/900
e.271/1000
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
From 100 to 199, the following numbers have one zero in them

101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 120, 130, 140, 150, 160, 170, 180, 190,
There are 18 numbers listed above



And there are 9 copies of this similar pattern (just change the first digit; eg: 201, 202, ... is another set, 301, 302, ... is another and so on...)


So there are a total of 9*18 = 162 numbers from 100 to 999 that have one number in them


The following numbers have two zeros in them
100, 200, 300, 400, 500, 600, 700, 800, 900


and there are 9 numbers listed above


So there are a total of 162 + 9 = 171 numbers that have at least one zero


So the probability is 171/900 since there are 900 numbers from 100 to 999 (because 999-100+1 = 900)


So the answer is choice D