100 coins with two sides (head and tail)
20 coins are fair (50% of getting head and 50% of getting tail)
80 coins are biased (70% of getting head and 30% of getting tail)
What is the probability of get head if we throw a randomly chosen coin from the 100 coins once I said .2*.5 + .8*.7 = .66
Now, given that we got a head, what is the conditional probability that the coin we threw was biased? This is tricky for me as to how to set it up. I understand that the formula is P(A|B) = P(A intersect B)/ P(B)
but im not sure how to get P(A intersect B) or P(B) or how to assign those