The probability, that in a randomly selected 3 -digit number at least two digits are odd, is

Atleast two digits are  odd=Exactly 2 digits odd+exactly 3 digits odd

$$\begin{gathered} \text{ For exactly three digits are odd =5×5×5=125} \\ \text{ For exactly two digits odd : } \\ \mathrm{If} 0 \mathrm{is} \mathrm{used} \mathrm{then} \mathrm{no} \mathrm{of} 3 \mathrm{digit} \mathrm{numbers} \mathrm{with} 2 \mathrm{odd} \mathrm{digits}=2\times 5\times 5=50 \\ \mathrm{If} 0 \mathrm{is} \mathrm{not} \mathrm{used} \mathrm{then} \mathrm{no} \mathrm{of} 3 \mathrm{digit} \mathrm{numbers} \mathrm{with} 2 \mathrm{odd} \mathrm{digits}{=}^3{\mathrm{C}}_1\times 4\times 5\times 5=300 \\ \text{ Required Probability }=\frac{125+50+300}{900}=\frac{475}{900}=\frac{19}{36} \end{gathered}$$