60 ELEMENTARY PROBABILITY Ch. 3 



Another method of classifying human bloods is based on the M 

 and N factors, which are inherited independently of the A and B 

 factors; that is, the genes for M and N are on a different pair of 

 chromosomes from that which carries the gene for A and B. Appar- 

 ently, both M and N are never both absent. There are, therefore, just 

 three types: M, N, and MN if we ignore the subtypes which have 

 been discovered recently. The following symbolism will be employed 

 in the discussion of the M-N blood types: 



M/M = type M, N/N = type N, and M/N = type MN. 



The inheritance of these types can be studied in the manner already 

 established for the A-B blood groups. 



In view of the fact that the three M-N types are classifications 

 which are independent of a person's A-B type, the two blood group- 

 ings considered simultaneously make it possible to distinguish 

 3 x 4 = 12 different blood types even without bothering with the 

 subdivisions of the A-B and M-N groups, which are serologically 

 determinable. 



Problem 3.12. If a woman's blood belongs to types and MN, and her hus- 

 band's blood is AB and N, what are the possible blood types for their first child, 

 and what is the probability associated with each type? 



The mother can pass on to her child one of the pairs of genes 

 0, M or 0, N because her genetic constitution as regards blood types 

 is (O/O) (M/N). Likewise, the father can transmit either A, N or 

 B, N to his offspring. Therefore, the possible gene combinations in 

 the child are: 0, M with A, N; 0, M with B,N;0,N with A, N; and 

 0, N with B, N. This makes the following four classifications of 

 bloods possible for their first child: A-MN, A-N, B-MN, and B-N, 

 each being expected to occur equally frequently. Hence, each of these 

 four classifications has a probability of one-fourth occurrence in 

 their first child. No other type can occur. 



Two other general blood groups will be mentioned: one involves 

 the Rh factor, the other is based on the P factor. Each is inherited 

 independently of the other and of the A-B and M-N types. Recent 

 discoveries of subdivisions of these groups will be ignored. There- 

 fore, P+ and P— groups will be recognized, and also Rh-f- and Rh — 

 types. Genetically, PP and Pp are P+, and RhRh and Rhrh are 

 Rh+, leaving pp as P— and rhrh as Rh — . 



