Give formulas for, and identify. the probability law of each of the following numerical valued random phenomena: (i) The number of defectives in a sample of size 20, chosen without replacement from a batch of 200 articles, of which 5 % are defective. (ii) The number of baby boys in a series of 30 independent births, assuming the probability at each birth that a boy will be born is 0.51. (iii) The minimum number of babies a woman must have in order to give birth to a boy (ignore multiple births, assume independence, and assume the probability at each birth that a boy will be born is 0.51). (iv) The number of patients in a group of 35 having a certain disease who will recover if the long-run frequency of recovery from this disease is 75% (assume that each patient has an independent chance to recover).