This material was created for use as a possible project in a Senior Seminar. This talk will be very accessible for undergraduates. The required background is calculus and Laplace transforms. The needed number theory will be given in the talk. Let x be a U(0,1) random variable. Express x as a continued fraction. x = [0;a(1),a(2),a(3),...]. We will find an expression for P(a(n)=k). Next we will closely examine P(a(2)=k). If time permits an expository discussion will be given for the asymptotic case.