Bayesian Inference with Unreliable Witnesses

Medium probability interview practice: Bayesian Inference with Unreliable Witnesses.

In London, the probability of rain on any given day is **p = 0.5**. You have 3 friends who each independently tell you about the weather. Each friend tells the truth with probability 2/3 and lies with probability 1/3. If all three friends tell you it is raining, what is the probability that it is actually raining?

• All problems