128 COMPLETION OF THE GENETICS EXPERIMENT 



Exercise XXV 



probability of "box cars" is the product of the 

 probabilities of turning up a six on each die 

 separately (1/6), or/' = 1/6 X 1/6 = 1/36. 



Genetics makes frequent use of this principle. 

 At fertilization an egg and a sperm combine 

 randomly. For any genetic trait, the egg may 

 contain either a dominant or a recessive gene, 

 and likewise the sperm may contain either a 

 dominant or a recessive gene. If one considers 

 that the probability of an egg containing a 

 dominant (or recessive) gene is 0.5, the same is 

 true for the sperm. The probability, then, that 

 the fertilized egg (zygote) will contain two 

 dominant genes is the product 0.5 X 0.5, or 

 0.25. That is, in a suitably large population of 

 offspring, 25% will carry two dominant genes 

 (homozygous dominant). Likewise, 25% can 

 be expected to carry two recessive genes (homo- 

 zygous recessive). Another 25% of the offspring 

 will receive a dominant gene from the father 

 and a recessive from the mother; in the final 

 25% this is reversed, and a recessive gene will 

 come from the father and a dominant from the 

 mother. Thus 50% of the offspring should 

 possess one dominant and one recessive gene 

 (heterozygous). 



Further coin-tossing tests help to illustrate 

 the probability of occurrence of joint inde- 

 pendent events such as these. 



(a) Toss two coins at a time 12 times, and 

 record the results: (h, h); (h, t); (t, t). Now 



using the principle that P^^y = Px X Py, calcu- 

 late the probability of each paired outcome (2 

 heads, 2 tails, or a head and a tail). How 

 closely do the results agree with the theoretical 

 prediction? You might try tossing the two 

 coins 100 times to see if the agreement is better. 



(b) Repeat the above test tossing three coins 

 16 times. Calculate the probability of each com- 

 bination: (h, h, h); (h, h, t); (h, t, t); and (t, t, t). 



(c) Can you derive a general relationship 

 that could be used to predict the results when 

 n coins are tossed together a large number of 

 times? 



In a family with five children what is the 

 probability that all will be daughters? that all 

 will be of the same sex? (This is a problem in 

 either-or probability. Whereas the probability 

 that several events will all happen together is 

 the product of their several probabilities, the 

 probability that any one of several possible 

 events will occur is the sum of their separate 

 probabilities.) 



For a more complete treatment of the use of 

 statistical methods in heredity, consult any 

 modern textbook of genetics. The chapter on 

 "Statistical Inference in Genetics" in Principles 

 of Genetics, by Sinnott, Dunn, and Dobzhansky, 

 5th ed., McGraw-Hill, 1958, is particularly 

 recommended. 



EQUIPMENT 



equipment for handling Drosophila as in Exercise 

 XXII 



a hatching generation of Drosophila to illustrate 

 sex-linkage. Although apricot, cut, and bar have 



been used as markers in the exercise here, many 

 others will serve. Details can be found in any 

 genetics text or in the Drosophila Guide mentioned 

 in Exercise XXII. 



