How to combine probabilities for guesses

Question

Let 3 people guess an object A or B. Each person have 80% chance of being correct.

What is the probability of object being an A, if:

• all 3 of them say it is an A
• only 2 say it is an A

Can you please also refer to generalised version of this question?

EDIT: chance for A or B is 50/50

Answer 1

Assume guesses are independent:

First case - the probability that all three are wrong is $.2^3=.008$.

Second case - the probability that two are wrong and one is right is $.2^2\times .8$ for each, so total is $3\times .2^2\times .8=.096$.