Your friend Andy claims to have ESP (extra-sensory perception). To test this claim, you propose the following experiment: You select one of four cards and Andy tries to identify it using his ESP. Let denote the probability that Andy is correct in identifying the card. Suppose that the experiment is repeated ten times and Andy is correct four times and incorrect six times.

a. What would the null hypothesis be in this situation?

c. Come up with 2 prior distributions for that you can use for this problem. Make sure to justify why you think that prior distribution is reasonable to use.

d. Based on your prior distributions, find the posterior probabilities that Andy has no ESP ability?