[Math] the probability that you toss next time, heads turns up

probability

A bag contains 5 coins. Four of them are fair and one has heads on
both sides. You randomly pulled one coin from the bag and tossed it 5
times, heads turned up all five times. What is the probability that
you toss next time, heads turns up. (All this time you don't know you
were tossing a fair coin or not).

Best Answer

Alternately, you could fully build the tree. What is the probability that you picked a fair coin? What is the probability that it shows heads five times in a row? The unfair coin? Five times in a row?

And don't forget conditional probability.