Suppose that a statistician is interested in H0:/x = 50 and Hi'.fx 9^ 50. His prior distribution consists of a mass of probability of .25 at /x = 50, with the remaining .75 of probability distributed uniformly over the interval from H = 40 to /x — 60. Find the prior probability that:

(a) 45 < ix < 55

(b) 47

(c) Ho is exactly true

(d) the hypothesis 49 < n < 51 is true.