Answer each part.

Problem 70: Bodies in the fridge ( vv ) My two friends, who shall remain nameless, but whom I shall refer to as P and Q, both told me this afternoon that there is a body in my fridge. I'm not sure what to make of this, because P tells the truth with a probability of p, while Q (independently) tells the truth with a probability of only q. I haven't looked in the fridge for some time, so if you had asked me this morning, I would have said that there was just as likely to be a body in the fridge as not. Clearly, in view of what my friends have told me, I must revise this estimate. Explain carefully why my new estimate of the probability of there being a body in the fridge should be 1-p-q+ 2pq I have now been to look in the fridge and there is indeed a body in it; perhaps more than one. It seems to me that only my enemy E, or my other enemy E, or (with a bit of luck) both E, and Ey would be in my fridge, and this evening I would have judged these three possibilities equally likely. But tonight I asked P and @ separately whether Er was in the fridge, and they each said that she was. What should be my new estimate of the probability that both E, and E, are in my fridge? Of course, I always tell the truth.Problem 51: Spherical loaf ( vVV ) A spherical loaf of bread is cut into parallel slices of equal thickness. Show that, after any number of the slices have been eaten, the area of crust remaining is proportional to the number of slices remaining. A European ruling decrees that a parallel-sliced spherical loaf can only be referred to as 'crusty' if the ratio of volume V (in cubic metres) of bread remaining to area A (in square metres) of crust remaining after any number of slices have been eaten satisfies |