Final answer:
The probability that a certain proportion of offspring will be produced with particular characteristics is most commonly determined using a Punnett square, which applies the product rule from probability theory.
Step-by-step explanation:
To determine the probability that a certain proportion of offspring will be produced with particular characteristics, you would typically use a Punnett square. This is a visual tool derived from the laws of probability, allowing you to predict the possible offspring from a cross between two parents. It incorporates the product rule, which calculates the likelihood of two independent events occurring together by multiplying their individual probabilities. The product rule is useful when you are considering scenarios where two or more characteristics must be present simultaneously (think 'and').
If you were interested in the chance of occurrence of any one of several traits, then the binomial expansion equation could also be employed, especially for more complex scenarios involving multiple offspring and a larger number of allele combinations.
The Chi square test is another tool that can be used to determine the likelihood that an observed ratio is due to chance, comparing observed proportions with expected ratios from a hypothesis (such as those derived from a Punnett square). It is not used for predicting proportions but for testing hypotheses against observed data.