1) the probability of ending up in the set of winners is

1/billion

2) the probability of being (a specific) one of the trillion is

1/(b * t)

the probability of being a 2) given you are awake is

p(2 | awake) = P(awake | 2) * p(2)

                    p(awake)


            = 1 * 1E-21
              ---------
                   1



            = very small