2003 AMC 12A Problem 8

The number $60$ has $12$ positive factors: $1,2,3,4,5,6,$ $10,12,15,20,30,60.$ Six of them are less than $7,$ namely $1,2,3,4,5,6,$ so the probability is $\dfrac{6}{12}=\dfrac12.$ Thus, the correct answer is E.