Zeros on a roulette wheel: we now wish to make a more sophisticated estimate of the number of zeros on a roulette wheel without looking at the wheel. we will do so with bayesian inference. recall that when a ball on a roulette wheel falls into a non-zero slot, odd/even bets are paid, when it falls into a zero slot, they are not paid. there are 36 non-zero slots on the wheel. we assume that the number of zeros is one of {0,1,2,3). we assume that these cases have prior probability 0.1,0.2,0.4,0.3). (a) writen for the event that, in a single spin of the wheel, an odd/even bet will not be paid (equivalently, the ball lands in one of the zeros). write z for the number of zeros in the wheel. what is p(n|z) for each of the possible values of z (i. e. each of {0,1,2,3})? (b) under what circumstances is p(z = 0 observations) not 0? (c) you observe 36 independent spins of the same wheel. a zero comes up in 2 of these spins. what is p(zlobservations)?