Next May, an ornithologist intends to trap one male cuckoo and one female cuckoo. The mass M of the male cuckoo may be regarded as being a normal random variable with mean 116 g and standard deviation 16 g. The mass F of the female cuckoo may be regarded as being independent of M and as being a normal random variable with mean 106 g and standard deviation 12 g. Determine

(a) the probability that the mass of the two birds together will be more than 230 g.

(b) the probability that the mass of the male will be more than the mass of the female. By considering X-9M-16F, or otherwise, determine the probability that the mass of the female will be less than nine-sixteenths of that of the male. Suppose that one of the two trapped birds escapes. Assuming that the remaining bird will be equally likely to be the male or the female, determine the probability that its mass will be more than 118 g (C)