524 



MM' I \DI\ 



expect to have the following genetic 

 constitution :.!/->? .1/' plus <//^. J 

 A. 8. When placed in an iodine solution, 

 one allele causes pollen to stain blue 

 ,iikI another allele causes it to stain 

 red. Pollen from the hybrid is ob- 

 tained and stained. 



Sample 1 is \W) grains, of 

 which 30 are blue and 70 red. What 

 do you conclude regarding the ex- 

 pected 1 : 1 ratio? 



(b) Sample 2 is 150 grains, of 

 of which 81 are blue and 69 red. 

 What arc your conclusions regarding 

 this sample and the 1 : 1 ratio? 



(c) Combine the data in samples 1 

 and 2, and test against a 1:1 ratio. 

 What do you conclude? Is this pro- 

 cedure permissible? Is it desirable? 

 Explain. 



A. 9. You want to test whether a particular 

 penny is unbiased by tossing it 100 

 times. How can you tell if the coin 

 is biased? 



A. 10. In a population of 1000 chickens, 

 only 250 are homozygous for the gene 

 pair (WW) producing w r hite feathers. 

 Assuming genetic equilibrium, what 

 do you calculate to be the frequency 

 of W in the gene pool? Give 



(a) your best single estimate, and 



(b) your estimate with 95% con- 

 fidence. 



C. Specific Probabilities Expected 

 From Parameters Involving One 

 Variable (Figure A-1C) 



Without tossing an unbiased penny, one 

 can assign a value p = 0.5. Without re- 

 course to trial, one can propose the hypoth- 

 esis that p = Y% that a particular side of 

 an unbiased octahedron will fall down. 

 Similarly, the probability that an unbiased 

 die will fall with a given side up is Y>- In 

 such cases one has no difficulty in deciding 



upon the probability of success. At other 

 times one does not know the probability 

 ot success, and this parameter must then 

 be determined. 



1. Rules of Probability 



a. The addition rule. Sometimes a suc- 

 cess can occur in two or more different ways, 

 each way excluding the others. What is 

 the total probability of success in such 

 cases? 



If on a single toss of a die the probability 

 of a "one" is J/£ and the probability of a 

 "two" is l ^, then the expectation or prob- 

 ability of either a "one" or a "two" is 

 Y + Y — Y- In general, the probability 

 that one of several mutually exclusive suc- 

 cesses will occur is the sum of their indi- 

 vidual probabilities. If the probability 

 that an event will succeed is p, and the 

 probability that it will fail is q, then the 

 probability of either success or failure is 

 p + q. But if it is certain that the event 

 must either succeed or fail, then p -f- q = 1, 

 p = 1 — q, and q = 1 — p. 



b. The mi duplication rule. Sometimes 

 over-all success depends upon the occur- 

 rence simultaneously or consecutively of 

 two or more successes, and the occurrence 

 (or failure) of one success in no way influ- 

 ences the occurrence (or failure) of the 

 others. 



If the probability of "one" in the toss 

 of a die is Y an d if the probability of 

 another "one" in a second toss is also Y* 

 then the probability of "one" on the first 

 and "one" on the second is ^ X ^ 

 = 3^6- I n general, the probability that 

 all of several independent successes will 

 occur is the product of their separate 

 probabilities. 



2. The Binomial Expression 



Given a parameter involving only one 

 variable, one can determine the exact prob- 

 abilities of obtaining specific combinations 



