i just ran a quick test and it came up with the following:
Here’s what we have at this time: The table below displays the probabilities of the alternatives prior to the new observation(s). It also illustrates how the prior probabilities are combined with the conditional probabilities of alternatives by multiplying the prior probabilities by their respective conditional probabilities for the new observations. The resulting joint probabilities are then normalized to form the posterior probabilities of the alternatives (i.e., after the new observations are taken into account).
Alternative Prior probability of each alternative (before making new observations)
New observations: Conditional probability of each alternative when observing 3 more successes and 20 more failures
Joint probability (determined by multipling prior by conditional probability)
Posterior probability of each alternative (after observations are made)
A. i am a poet
0.941176 X 0.0000000000 = 0.0000000000 /sum = 0.000000
B. i am a poetaster
0.058824 X 0.0000922337 = 0.0000054255 /sum = 1.000000
sum = 0.0000054255
At this time, the total number of successes is 6 and the total number of failures is 21.
Conclusion at this time: ‘i am a poetaster‘.
Given this pattern of 27 observations, the conclusion would be in error 5 percent of the time. In other words, we would be 95 percent confident that this is the correct conclusion.
This assumes that the likelihood of success when Alternative A is true is 80 percent or higher, and the likelihood of success when Alternative B is true is 20 percent or lower.