Your friend tossed a fair coin when you weren’t around. she has a habit of messing with you every once in a while, and so there is a 1/3 chance that she will lie to you about the result of the coin toss (report heads as tails and tails as heads), and 2/3 chance that she will tell you the true result of the coin toss. suppose she claims that the coin toss resulted in heads. what’s the probability that she’s lying?