Attempts until Rnd<constant, has exponential distribution?

[Dodo]

Suppose a number U is generated from an uniform distribution [0,1].

If you repeat the process until U < some constant,
does the number of loops have an exponential distribution?

If so, could you point the way to a proof? Thanks in advance.

[matt grime]

no it isn't exponential, but this looks like homework, and is quite easy: write down the probability that the first pick less than, say, p occurs on the k'th turn and note which distribution you get.

[Dodo]

Hmm... Is there an emoticon for embarrasment here? :)

(google-google-google...)
http://mathworld.wolfram.com/GeometricDistribution.html (for attempts-1, i.e., failures until success)

Guess I only needed a little tap on the head to remove the spiderwebs.
Thank you!