Use Punnett squares and the multiplication rule.

Ana draws the classic 2×2 Punnett square to answer Dr Antonious’ question.

Ana: ‘If we look at this 2x2 Punnet square for two heterozygotes the probability for a sperm with the dominant allele A (from event X) to fertilize an oocyte with the dominant allele (from event Y) is ½ x ½ = ¼, because we want both gametes to have the dominant allele, but also the creation of each gamete is an independent event. 

So, we can modify the 2x2 Punnet square to add the probabilities for the gametes as follows:

And then further modify it to add the probabilities for the offspring:

And that will give us: 

• ¼ (25%) chance for AA

• ½ (50%) chance for Aa (because ¼ + ¼ = ½)

• ¼ (25%) chance for aa (affected)

Dr. Antoniou (smiling): ‘Excellent. That’s the multiplication rule which is used to calculate the probability of two independent events taking place at the same time. The probability of event X and event Y happening at the same time, is the product of their individual probabilities. For human genetics we can use the examples of fertilization of an oocyte by a sperm. The events of spermatogenesis (event X) and oogenesis (event Y) are independent of each other. So, if we have two heterozygous individuals (Aa), each gamete has ½ probability to carry the dominant allele A and ½ probability to carry the recessive allele a. Now, how do we find the probability that a child is either carrier or affected?’

Ana: ‘I’d use the addition rule: ½ (Aa) + ¼ (aa) = ¾ total for those outcomes.’

Michael: ‘I understand the multiplication rule but I am not clear what the addition rule is. Can you please explain?’

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