Sally has two coins. The first coin is a fair coin and the second coin is biased. The biased coin comes up heads with probabilit
y .75 and tails with probability .25. She selects a coin at random and flips the coin ten times. The results of the coin flips are mutually independent. The result of the 10 flips is: T,T,H,T,H,T,T,T,H,T. What is the probability that she selected the biased coin?
''What is the probability that she selected the biased coin?”
When we have n possible outcomes of an event and all of them have the same probability of appearance, then in theory each possibility has a probability 1/n of being the result of the event.
In this case the event is choosing randomly a coin out of 2, so no matter what the biased coin is or the results we get when we toss it, the probability of choosing the biased coin is ½ = 0.5 or 50%.
