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900 possible outcomes,

ones that have at least 1 zero: every ten and 100-109,200-209,300-309,...900-909

900/10 = 90

90+90=180

would this be right?

Notice that in each hundred....we have [ 10 + 9 ] = 19 integers that contain at least one zero

And there are 9 "blocks" of "hundreds" from 100 - 999

So.....the probability is :

[ 19 * 9 ] / [ 999 - 100 + 1 ] = 171 / 900 = [ 19/ 100 ]