If a committee of 3 is to be chosen from a group of 38 people of which you are a member. What is the probability that you will be on the committee?

From the given condition, it is clear that a particular person is always in a committee of 3 persons. 

it means, we have to select 2 person out of 37 person.
Required Probability $=\frac{{ }^{37}{\mathrm{C}}_2}{{ }^{38}{\mathrm{C}}_3}$