Problem set 1, Spring 2016
student name:
8 points total
Note: Please show your work and define your symbols clearly.
1. You roll a six-sided dice four times.
a) What is the probability of rolling four sixes?
1/6 X 1/6 X 1/6 X 1/6 = 1/1296
b) What is the probability of rolling no 1’s in four rolls of the dice?
(1 – 1/6) X (1 – 1/6) X (1 – 1/6) X (1 – 1/6) = 625/1296
c) What is the probability of rolling at least one 4?
This is the opposite of rolling no 4’s.
1 – P{no 4’s} = 1 – (5/6 X 5/6 X 5/6 X 5/6) == (1296 – 625)/1296 = 671/1296
2. You cross AaBbccDdEeFF X aaBbCCDdEeFf. In each case, capital letter denotes dominant,
A- gives phenotype A, aa gives phenotype a, and so on.
a) What is the probability of AaBBCcddeeFf offspring?
½ X ¼ X 1 X ¼ X ¼ X ½ = 1/256
b) What is the probability of getting offspring with the phenotype AbCDeF?
½ X ¼ X 1 X ¾ X ¼ X 1 = 3/128
3. In the plant C. spotrun, blue flowers are recessive to pink flowers and oval petals are
recessive to square petals. If a pure-bred plant with blue, square petals is crossed with a plant
that's heterozygous for pink, square petals, what are the genotypic and phenotypic ratios of
the F1 generation?
pink, square
Cross is bbOO X BbOo => ¼ BbOO
¼ BbOo
¼ bbOO
blue, square
¼ bbOo
½ pink, square and ½ blue, square
4. How is a test cross used to determine the genotype of an organism? If a test cross is
performed on a tall plant (tall = dominant) of unknown genotype, what must that plant's
genotype be if:
a) half of F1s are tall and half are short? Ss
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Problem set 1, Spring 2016
8 points total
b) the F1's are all tall? SS
student name:
5. You have discovered a rare, fresh water squid, J. gavadae, living in Lake Monroe. Further
investigation reveals two true-breeding strains, one with blue spots and short tentacles, and
one with yellow spots and long tentacles. In crosses between the two strains, the F1 offspring
always exhibit long tentacles and yellow spots. When you cross the F1's, you found 179 with
long tentacles and yellow spots, 58 with long tentacles and blue spots, 63 with short tentacles
and yellow spots and 20 with short tentacles and blue spots. What are the genotypes of the two
original strains? Define your genetic symbols clearly.
bbss = blue, short
BBSS = yellow, long
6. The state of Indiana participates in a multi-state lottery called Powerball. In powerball, a
player chooses 5 numbers from 1 – 49. In addition, a player chooses a single number from 1 –
42, which is called the powerball. The player must match the 5 numbers plus the powerball in
order to win the grand prize. What is the probability of winning the grand prize. You must
show your calculations (Note: This is an old version of powerball. Odds are lower now).
.
5/49 X 4/48 X 3/47 X 2/46 X 1/45 X 1/42 = 120/9,610,695,360 = 1/80, 089,128
(note: the powerball lottery has changed to further decrease the odds of
winning. This makes the jackpot bigger but each ticket even less likely to
match.)
7. You cross a true breeding red haired, blue eyed purple people eater with one that has green
hair and orange eyes (green hair and orange eyes are recessive) to produce doubly
heterozygous offspring. You cross the double heterozygous offspring to produce F2 progeny.
a) Please draw a Punnett square showing the genotypes of all of the offpsring.
GO
Go
gO
Go
GO
GGOO
GGOo
GgOO
GgOo
Go
GGOo
GGoo
GgOo
Ggoo
gO
GgOO
GgOo
ggOO
ggOo
go
GgOo
Ggoo
ggOo
ggoo
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Problem set 1, Spring 2016
student name:
8 points total
b) Use a branch diagram to determine the likelihood of getting offspring of the
genotype ggOo (where g is the allele that causes green hair when homozygous, o is the
allele that causes orange eyes when homozygous).
OO
gg (1/4)
¼ X ½ = 1/8
Oo (1/2)
oo
8. In your studies of the exotic field mouse, A. millerae, you find that there are two, true
breeding strains in the wild. The first strain has red fur, short legs and fuzzy tails, and the
second strain has brown fur, long legs and bare tails.
a. To understand the differences between these strains, you cross strain 1 X strain 2. All
of the offspring have red hair, long legs and fuzzy tails. You then cross the F1 animals
amongst themselves and find the results listed below. Please give the genotypes of each
of the F2 phenotypic classes.
425
138
142
135
51
47
46
16
1000
red fur, long legs, fuzzy tails
red fur, long legs, bare tails
red fur, short legs, fuzzy tails
brown fur, long legs, fuzzy tails
red fur, short legs, bare tails
brown fur, long legs, bare tails
brown fur, short legs, fuzzy tails
brown fur, short legs, bare tails
R–L–F–
R–L–ff
R–llF–
rrL–F–
R–llff
rrL–ff
rrllF–
rrllff
Note: You can see that the phenotypic ratio for each is 3:1. This indicates two alleles
of one gene regulating each phenotype with a simple dominant: recessive relationship.
b. What do you expect to see from a test cross involving F2 animals with red fur, short
legs and fuzzy tails? Please give the expected genotypes, phenotypes and their relative
frequencies.
Cross is R–llF– X rrllff
1/9 RRllFF X rrllff => RrllFf
2/9 RrllFF X rrllff => RrllFf and rrllFf
2/9 RRllFf X rrllff => RrllFf and Rrllff
4/9 RrllFf X rrllff
=> RrllFf, Rrllff, rrllFf, rrllff
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Problem set 1, Spring 2016
8 points total
student name:
So genotypes are 4/9 RrllFf, 2/9 Rrllff, 2/9 rrllFf and 1/9 rrllff
RrllFf is red furred, short legged, fuzzy tailed
Rrllff is red furred, short legged, bare tailed
rrllFf is brown furred, short legged, fuzzy tailed
rrllff is brown furred, short legged, bare tailed
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