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Using Rule of Multiplication and Addition for Punnett Squares
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In probability: The product rule: Refers to two independent events occurring together. So if I have two dice that I throw at the same time, and I want to find the probability of getting one 1 and one six, I would apply the probability rule (1/6*1/6 = 1/36). The sum rule: Refers to either one of two independent events occurring. So if I threw one die and I want to calculate the the probability of getting either a 1 or a six, I would use the sum rule (1/6 + 1/6 = 1/3).
Now, to apply these to genetics we have to understand what the question is actually asking. Say you are given a heterozygous cross Aa x Aa. If the question is asking to determine the probability the offspring will be recessive, we need to use the product rule, since are calculating the probability of an aa offspring. The two independent events are the parents sorting a recessive allele in the gamete, and that needs to happen at the same time to get a aa offspring. However, if the question is, what is probability of a dominant phenotype, you can have AA or Aa, so you would use the sum rule. In this case either one of those independent events will give us the result we are looking for.
Now, to apply these to genetics we have to understand what the question is actually asking. Say you are given a heterozygous cross Aa x Aa. If the question is asking to determine the probability the offspring will be recessive, we need to use the product rule, since are calculating the probability of an aa offspring. The two independent events are the parents sorting a recessive allele in the gamete, and that needs to happen at the same time to get a aa offspring. However, if the question is, what is probability of a dominant phenotype, you can have AA or Aa, so you would use the sum rule. In this case either one of those independent events will give us the result we are looking for.
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