GMAT Quantitative Reasoning Practice Test 1

Since three digits are zero, only 4 digits are left for consideration (of which, none is zero). Since 1 does not appear in the numbers, there are 4 even numbers (without 0 ), and 4 odd numbers (without 1 ) to choose from. The probability for every digit to be odd is $\frac{1}{2}$. There are 4 different ways to arrange 3 odd numbers and one even number in 4 places. Each of these ways has a probability of ${\left(\frac{1}{2}\right)}^4$. And together:
$4\times {\left(\frac{1}{2}\right)}^4=4\times \frac{1}{16}=\frac{4}{16}=\frac{1}{4}$.