You're finding a probability based on a group of independent events, so I'd suggest using beta distribution. The Wikipedia page gives how to find the mean and variance given alpha and beta. Decide what you think they are (you already effectively gave that the mean was 3%, so you just need the variance), and solve for alpha and beta. If you observe a success, increment beta, and recalculate the mean.

Also, you seem to be saying 1% failure at the beginning, and 3% later on. In addition, both of these would be much too high to risk a launch.