September 10 , 2013
Biology 2C03: Genetics
Probability & Punnett Squares
What is the Probability of a Trait (SCD) Appearing in the Offspring?
- From a biological point of view, we first need to know the probability of
alleles being distributed to the gametes
- Mendel’s Principle of Segragation:
1. Each individual organism possesses two alleles encoding a trait
2. Alleles separate when gametes are formed
3. Alleles separate in equal proportions
Punnett Square SCD: β β x β β S A
- Each parental allele has a ½ chance of being passed to a child
- Each combination of alleles (genotype) has a ¼ probability of occurring
- ¼ children are expected to have SCD
- 3 genotypes are expected in the children:
¼ β β : ½ β β : ¼ β β S S
- How many phenotypes are expected in the children:
Two phenotypes
¾ normal: ¼ SCD
A Quicker Primer in Probability
- Roll a die: Probability of rolling a 6 = P(roll a 6) = 1/6
Probability of rolling an even number = P(even) = 1/6 +1/6 + 1/6 = ½
Sum rule: the probability of the occurrence of any of the several
mutually exclusive events is the sum of the probabilities of the
individual events (either, or)
- Roll two dice:
Probability of rolling two 6’s = P(roll 2 6’s) = 1/6*1/6 = 1/36
Probability of rolling a 6 and a 4 = (1/6*1/6) + (1/6*1/6) = 1/18
Product rule: the probability of two independent events happening
simultaneously is the product of their individual probabilities (and)
- If diploid individuals carry two alleles, we can liken this to a flip of a coin
with two sides:
Probability of flipping a head = P(heads) = ½
Probability of flipping a tail = P(tails) = ½
S A
A person is diploid (two copies of the genome), e.g. β β
During meosis, a gamete (haploid) receives just one allele
Probability of a gamete receiving β = P(β ) = ½
Probability of a gamete receiving β = P(β ) = ½
- Coin flip simulation: first few flips, probability of heads fluctuates, but given
enough trials, the probability tends towards P = 0.5
- Due to biological fluctuation, this will also be true of the inheritance of alleles
- Repeat this enough times and you see a normal distribution: 100 flips, most
common event would be 50 heads, 50 tails. But should not be surprised to
see 49:51 or 52:48
- Towards the left and right, it is much less likely to see these ratios Probability Can be Used Where One of Two Alternative Outcomes is Possible During
Each of a Large Number of Trials
- Example: the probability of having two boys? P= (½)(½)= ¼
The probability of having one boy and one girl must take into account
that this can occur in two ways, P = (½)(½) + (½)(½) = ½
Probability of having four boys? P= 1/16
But, say a family has four boys, what is the probability that their next
child will be a boy? P= ½, these are independent events
Mendel’s Concept of Dominance
- This 3:1 phenotypic ratio is a Mendelian ratio – for a recessive disorder
- In Mendel’s st

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