he rules of probability can be applied to Mendelian crosses to determine the expected phenotypes and genotypes of offspring.
KEY POINTS
The Product Rule is used to determine the outcome of an event with two independent events; the probability of the event is the product of the probabilities of each individual event.
The Sum Rule is used to determine the outcome of an event with two mutually exclusive events from multiple pathways; the probability of the event is the sum of the probabilities of each individual event.
The Product Rule of probability is used to determine the probability of having both dominant traits in the F2 progeny; it is the product of the probabilities of having the dominant trait for each characteristic.
The Sum Rule of probability is used to determine the probability of having one dominant trait in the F2 generation of a dihybrid cross; it is the sum of the probabilities of each individual with that trait.
TERMS
probability
a number, between 0 and 1, expressing the precise likelihood of an event happening
product rule
the probability of two independent events occurring together can be calculated by multiplying the individual probabilities of each event occurring alone
sum rule
the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities
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Probability Basics
Probabilities are mathematical measures of likelihood. The empirical probability of an event is calculated by dividing the number of times the event occurs by the total number of opportunities for the event to occur. Empirical probabilities come from observations such as those of Mendel. An example of a genetic event is a round seed produced by a pea plant. Mendel demonstrated that the probability of the event “round seed“ was guaranteed to occur in the F1 offspring of true-breeding parents, one of which has round seeds and one of which has wrinkled seeds. When the F1 plants were subsequently self-crossed, the probability of any given F2 offspring having round seeds was now three out of four. In other words, in a large population of F2 offspring chosen at random, 75 percent were expected to have round seeds, whereas 25 percent were expected to have wrinkled seeds. Using large numbers of crosses, Mendel was able to calculate probabilities and use these to predict the outcomes of other crosses.
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