Basic Principles Group Problems (1)
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Biology 3500
Basic Principles Group Problems
Definition of probability: the chance that some event will occur.
e.g. What is the probability that the sun will rise in the east? 100% or 1 out of 1.
What is the probability that a tossed coin will land heads up? 1 out of 2 = 1/2 = 50%
% = percent = number of times out of 100 samples.
Percent can be derived by multiplying a fraction by 100. For example: 1/2 X 100 = 50%
In genetics, we will do a lot of calculations based on “probabilities.” We will do calculations that predict the probability of the simultaneous
occurrence of two independent events. For instance: What is the chance that two coins, tossed independently, will both come up heads? To come up with the answer we use the “
Product Rule
” which states: The probability of two independent events occuring simultaneously
can be determined by multiplying the probabilities of each independent event.
For two coins:
p(1
st
coin = heads) = 1/2
p(2
nd
coin = heads) = 1/2
p(both coins = heads) = 1/2 X 1/2 = 1/4
Note there are 4 possible outcomes for two coins being tossed: 2 heads in a row, 2 tails in a row, 1
st
coin heads and 2
nd
coin tails, or 1
st
coin tails and 2
nd
coin heads. So 1/4 is just the chance of 1 out of 4 equally likely outcomes. Situations where the Product Rule
is used can usually be stated as “AND” statements: What is the probability that the first coin will land heads up, AND the second coin will also land heads up?
We will also do calculations to determine the probability of either one or the other of two mutually
exclusive
events. For instance: What is the probability of a tossed coin coming down either heads
or tails? To do this calculation we use the “
Sum Rule
” which states: The probability of either one
or the other of two mutually exclusive
events can be determined by adding the probabilities of each event together. For the example above: p(coin toss = heads) = 1/2
p(coin toss = tails) = 1/2
p(both coins = heads or tails) = 1/2 + 1/2 = 1 (the coin will land either heads or tails). Situations where the Sum Rule
is used can usually be stated as “OR” statements: What is the probability that the first coin will land heads up, OR tails up?
The first problem set is on the reverse of this page. Try using the above rules to answer the questions. The problem set will be due this Friday.
Biology 3500
Basic Principles Problems
1.
(2 points) Two red eyed fruit flies are mated to each other. They produce 173 red eyed offspring and 59 brown eyed offspring.
a.
Is red dominant or recessive to brown?
Dominant
b.
What are the genotypes of the two parents?
Heterozygous Dominant for both parents c. What is the probability that the next single offspring produced by the two parents will have brown eyes?
1/4
2. (3 points) A hornless bull is mated to three cows. Cow A is hornless and has a horned calf.
Cow B is horned and has a horned calf. Cow C is horned and has a hornless calf.
a. Which allele is dominant horned or hornless?
Hornless b. What are the genotypes of the four adults? (use a capital H to denote the dominant allele.
Bull: Hh
Cow A: Hh
Cow B: hh
Cow C:hh
c. If the mating to cow B was repeated many times what ratio of phenotypes would you expect in the offspring?
1/2 Hornless, 1/2Horned 3. (7 points) In rabbits black fur (B) is dominant to brown fur (b) and long hair (L) is dominant to short hair (l). Two black long haired rabbits were mated and they produced 44 F
1
progeny: 25 black, long haired progeny; 9 brown long haired progeny; 7 black short haired progeny and 3 brown short haired progeny. a. What are the genotypes of the parents? BbLl and BbLl
b. How many types of gametes can each one produce? Please list them. 4 types of gametes BL, bl, Bl,bL
c. Four different genotypes are expected in the black, long haired class of offspring. Please list them. (The branching method (preferred) or a Punnett square will help with c. and d.).
BBLL,BbLl,BBLL, BBLl
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