You are considering whether to invest some money in
the Bitcoin market. You first talk to one of your friends and she claims that the price
of Bitcoin will go up. However, based on the past experience you have deduced that
your friend’s advice turns out to be true only 60% of the time. You also know that
thus far the price of bitcoin has gone up only 20% of the time. Assume that the
probability that your friend’s advice is correct and the probability that the price of
bitcoin will actually go up are independent. Given that your friend claims the price of
bitcoin will rise, what is your updated belief (probability) that the price of Bitcoin will
go up?
Clarifications:
A = price of bitcoin goes up (true or false)
B = friend's advice is bitcoin price will go up (true or false)
C = friend's advice is accurate (true or false)
P(C = true) is always 0.6 and is independent of whether the price of bitcoin goes up or down. The independence is not related to event B.
So far I've gather that we are looking to calculate P(A|B), however, I don't see any way to calculate this as we are conditioning on event B for which we have zero information. What am i missing here?
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