by mike

Inspired by this post by flagamuffin, here's a probability problem I found interesting...

You have in your pocket two coins. One is a normal fair coin, and one is a fake coin that has "heads" on both sides.

You reach into your pocket and take one of them at random. You toss it one, two, three times. One each flip, the coin comes up heads.

What is the probability that the coin will land heads on the next flip?