Probability

Probability Level 3

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?

81 900 \dfrac{81}{900} 90 900 \dfrac{90}{900} 171 900 \dfrac{171}{900} None of them \text{None of them} 190 900 \dfrac{190}{900}

Terry Yu by Terry Yu , 17, USA

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1 solution

Terry Yu
Jun 2, 2017

There are 900 900 numbers and in 100 − 199 100-199 , there are 19 19 zeroes. Since there are 9 9 of the identical set, that means the probability is 19 × 9 900 \dfrac{19 \times 9}{900} making the answer 171 900 \large\color{#20A900}\boxed{\dfrac{171}{900}} .

Note: It is also 19%, but I chose not to simplify it for the means of the problem in case someone divided wrong but got the right fraction.

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