1. Chance and the Distribution.of Families.In genetic experiments with plants and other animals, the most direct inferences asto method of inheritance come from a count of the progeny. For example, if one'were to make a cross betwee~ two pure lines. intercross the FJ,and from the inter-. cross obtaip approximately three-fourths ofone parental type and one-fourth of theother in thl! F z, a simple Mendelian model. one locus witbJ'P...".aJJeJes...!'lnd-c1Qmi.". ,-llilllc.e-~oJJiJ1..b.elI1kII.~~ This conclusion would be reinforced if the backcross ofan Fr hybrid (to the pure-line parental type that had not appeared in the F 1) pro.:duced progeny of which approximately one-half resembled the. aforementioned;parental ty)X's and one-hctlf the Fr hybrid. In man, the number of progeny from any single family is usually so ;m~ll that. these conclusions would not be warranted. A mating of two .heterozygotes for a. recessive defect can produce 4:0, 2:2, I :3, and 0:4 ratios, as ,well as the expected J: I, in families offour children. Similarly, the mating A/a X a/a having two chil dren, can produce 2:0 and 0:2 ratios as well as the expected 1:1. A bit ofreflection will convince the reader that this is not surprising. Consider., . for example, the couple with genotypes A/a and a/a, respectively, having two chil dren. Genetic theory expects them to have one A/a child and one a/a child because the A/a parent is expected to produce 1/2 A gemetes and 1/2 a gametes. ffthe A/a. parent is the male, this ratio will usually be realized among the sperm. Is there,' however, any guarantee that these"sperm will take turns, so to. speak, in fertilizing the egg'! Obviously not. The sperm involved in producing the two children could. well be A sperm in both cases or a sperm in both. If the A/a parent is the female, , there is not even a guarantee that the gametic ratio will be 1/2 A and 1/2 a, since! each meiosis ordinarily produces only one gamete and the various meioses are independent events: what happens in one meiosis does not influence what is tohapperl the next or any subsequent one. Hence, it could happen easily that the two'children of this A/a X a/a mating are both A/a or both a/a.Clearly the prediction of genetic results is fraught with uncertainties, eventsover which no one has control. Such uncertainty is generally referred to as'"chance." One author has recognized the large element of chance involved byenti.t1ing his book