I have n coins, where n-1 are fair and one is biased, showing tail on both sides. I want to ascertain whether the coin is fair by throwing k-times. If I get k-times tail, I decide it is biased. The question is :
What is the probability that this way of determination is false?
W( determination is false ) C(biased coin) T(throwing T k-times)
The solution is :
P(W) = P(¬ C,T) +P(C, ¬ T)
I am not sure why do we care for the probability of not getting tail with a biased coin. Why don’t we determine the probability of W like this:
P(W) = P(¬ C,T) +P(C, T)