GENE105
Probabilities
September 28, 2006
Punnet squares: The number of squares needed is 4n, where n is the number of traits
being followed.
2 traits, n=2 so the number of boxes is 42 or 16
4 traits, n=4 so the number of boxes is 44 or 256
Bottom line - the crossing square is too big to follow large numbers of traits!!!
An easier way to predict genotypes and phenotypes in crosses, as long as the dominance
relationships are known and the genes assort independently, is to use PROBABILITY
Probability - is the likelihood that an event will occur.
No chance of event occurring
probability = 0
(chance of rolling 10 on a six-sided die)
Event always occurs probability = 1
(chance of rolling 1,2,3,4,5,or 6 on a six-sided die)
****Probabilities of all possible events must add up to 1.****
The probability of an event =
# of chance of event
total # of possible events
Multiplication or Product Rule: The chance of two independent events occurring equals
the product of the chance that either event will occur.
The probability of independent events is calculated by multiplying the probability of each
independent event. You can predict the chances that parents with known genotypes will
produce an offspring of a particular genotype.
?What is the probability of tts's' offspring from the cross TtSs' x TtSs'?
Simplify the problem by resolving it into its component parts. First, what is the
probability of tt progeny? Draw a Punnet square depicting inheritance of T and t alleles
with the parental gametes on the top and left sides.
chance of inheriting tt = 1/4
Next, what is the probability of s's' progeny?
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GENE105
Probabilities
September 28, 2006
chance of s's' = 1/4
So the probability of tts's' is (1/4 x 1/4) or 1/16
Check the answer using the Punnet square for the dihybrid cross.
TS
Ts
tS
ts
TS
TTSS
TTSs
TtSS
TtSs
Ts
TTSs
TTss
TtSs
Ttss
tS
TtSS
TtSs
ttSS
ttSs
ts
TtSs
Ttss
ttSs
ttss
Recap: Multiplication Rule - the probability of independent events is calculated by
multiplying the probability of each independent event.
Addition or Sum Rule: The probability of dependent events occurring is calculated by
adding the probability of each event.
?What is the probability that a progeny of cross TtSs' x TtSs' will inherit a T
allele?
Remember that two types of progeny represent those who inherit a T allele, TT and Tt, so:
Probability of TT
=1/4 +
Probability of Tt
=1/2
Answer
=3/4 (or 75 per cent)
(The Punnet square for the dihybrid cross shows that 12 out of 16 inherit a T allele.)
?What is the probability that the progeny of the TtSs' x TtSs' cross will inherit a
copy of T and a copy of S? Hint: Here use the product rule and the sum rule.
Probability of inheriting T = (1/4 chance of TT +1/2 chance of Tt) or 3/4
Probability of inheriting S = (1/4 chance of SS +1/2 chance of Ss') or 3/4
The probability of inheriting 1 copy of T and 1 copy of S equals 3/4 X 3/4 or 9/16.
Look at the expected progeny from the dihybrid cross of TtSs' X TtSs' to convince
yourself of the calculated probability of the above problems.
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