Question 256025: 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?
a) 19/900 b) 81/900 c) 90/900 d) 171/900 e) 271/900
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! FIrst we have to find the total number of integers in the set: 999-100+1 = 900.
Next we need an organized way to determine our successful options: 0 in at least 1 digit.
0 in 3 digits:
0
0 in 2 digits:
100, 200, 300, 400, 500, 600, 700, 800, 900 = 9
0 in 1 digit:
101 - 110, 120, 130, 140, . . ., 190: 18
201 - 210, 220, 230, 240, . . ., 290: 18
. . .
901-910, 920, 930, 940, . . . 990: 18
or 18*9 = 162
Now 0 +9 + 162 = 171
So the probability is
171/900 = 19/100
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