GENETICS - BIOL 7    Quiz 7        October 3, 2006        NAME:  key

1.  Consider a situation in which events occur in clusters of six.  This could be “family of six”, or throwing a die six times, or throwing six coins at the same time, for example.  Write the binomial expansion that describes the possible outcomes of random independent events in clusters of six.  Be sure to state the meanings of each place keeper (i.e.  Let a = ...)

let p = probability or event x;   let q = probability of event “not x”  ==>     p + q = 1

1n = (p + q)n  =>  16 = (p + q)6

1 = p6 + 6p5q + 15p4q2 +20p3q3 + 15p2q4 + 6pq5 + q6

each term = probability of x instances of event x out of n total attempts:   nPx

2.  What is the probability of the following combinations in a family of 4 offspring from two parents heterozygous at all loci under study  (always assuming no cheating or "unfair" circumstances).  Show the relevant and simplest possible Punnett square for each cross: [put actual answer on the line; show work for possible partial credit]

                                             probability   

a.  2 females           6 * (½)^2 * (½)^2 = 6/16 = 3/8

a'.  3 females          4 * (1/2)^3 * (1/2) = 4/16 = 1/4

b.  2 dominant        6 * (3/4)2(1/4)2 = 6*9/256 = 54/256 = 27/128 
phenotype offspring
(one locus)

c.  2 recessive            6 * (3/4)2(1/4)2 = 6*9/256 = 54/256 = 27/128    
phenotype offspring
(one locus)

d.  2 offspring with       6 * (6/16)2(10/16)2 = 21600/65536 = .33 
dominant phenotype
at one locus and recessive phenotype
at the other locus (2 loci)

Punnett squares:  Aa * Aa for (b) & (c)
                          AaBb * AaBb  for (d)