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Department of Biological and Environmental Sciences
Genetics
 Dr. David A. Johnson
Biol 333    4 Credits   Spring 2017  MWF 8:00-9:05 AM   PH 204

Probability and Statistics

A Quick Overview of Probability and Statistics in Genetics: Probability and statistics are used to analyze genetic data and to predict outcomes. In predicting the outcome of a cross, first ask yourself, "What gametes (and in what proportion) do the parents make?"

  • Some Simple Concepts of Probability
    • Probability: The probability of an event is the number of "favorable" outcomes divided by the number of possible outcomes (assuming all outcomes are equally likely).
    • Probability of Independent Events: Two events are independent if the outcome of one event does not influence the outcome of the other event. The probability of two independent events occurring is the product of the two separate event probabilities (and = x).
    • Probability of Mutually Exclusive Events: Two events are mutually exclusive if only one of the two events can occur. The probability of one of two mutually exclusive events occurring is the sum of the separate event probabilities (or = +).
    • Binomial Expansion*: This can be used to calculate the probability of a combination of two independent events occurring. (A problem)
  • Chi-Square Goodness-of-Fit Test: This statistical test is used to determine how close a set of numbers is to an "expected" ratio. This test takes a set of numbers and asks how good it fits an expected ratio (like a 9:3:3:1 expected ratio). It calculates the probability of getting as bad or worse a fit to your expected ratio (P). Chi-square is defined as:
    • Σ((observed - expected)2)/expected
    • The degrees of freedom (df) is n-1 where n is the number of classes

*Binomial Expansion in Genetics

The expansion of a binomial equation (from algebra) is used to calculate the probability of multiple outcomes in genetics. A binomial equation is the sum of two numbers raised to a power, like:
(p+q)2
or
(p+q)3

If you remember your basic algebra, (p+q)2 = (p+q)x(p+q) = p2 + 2pq + q2
Similarly
(p+q)3 = p3 + 3p2q + 3pq2 + q3
and
(p+q)4 = p4 + 4p3q + 6p2q2 + 4pq3 + q4
or in general:
(p+q)n = pn + c1pn-1q + c2pn-2q2 + c3pn-3q3 + ... + qn
So, the expansion of the binomial is simply arrived at by writing the factor with p raised to the nth power (for example, 4th power for (p+q)4), plus p raised to the (n-1) power times q, plus p raised to the (n-2) power times q2, etc., until you get to the last factor qn.

Now, to find the coefficients of each factor (c1, c2, c3, etc.), use Pascal's Triangle.