How to solve advanced probability problems in Genetics
Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes’ relative likelihoods and distributions. In common usage, the word “probability“ is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.
There are several competing interpretations of the actual “meaning“ of probabilities. Frequentists view probability simply as a measure of the frequency of outcomes (the more conventional interpretation), while Bayesians treat probability more subjectively as a statistical procedure that endeavors to estimate parameters of an underlying distribution based on the observed distribution.
A properly normalized function that assigns a probability “density“ to each possible outcome within some interval is called a probability density function (or probability distribution function), and its cumulative value (integral for a continuous distribution or sum for a discrete distribution) is called a distribution function (or cumulative distribution function).
Problem:
Achondroplasia is an autosomal dominant genetic disorder, while red green color blindness is an X-linked recessive disorder. For a given population, the frequency of achondroplasia is 1 in 25,000. If red green color blindness affects 9% of males, what percentage of the population would you expect to be:
1) Color blind male and normal height?
2) Color blind females and normal height?
3) Males with normal vision and achondroplasia?
4) Females with normal vision and achondroplasia?
5) Males with both color blindness and achondroplasia?
6) Females with both color blindness and achondroplasia?
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