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

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) (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
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