1 Probability1

# 1 Probability1 - Basic Probability Theory Genetics has a...

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Basic Probability Theory • Genetics has a large random component – Which allele does a parent transmit to their offspring? – Will an offspring display the disease if both parents are carriers? • Hence, an understanding of probability is critical to a complete understanding of genetics • Genomics has become largely statistical in nature Overview • Events and Probabilities • Rules of probabilities – Prob sum to one – And or Or rules • Conditional probability – Conditional probabilities – Bayes theorem • Application: Disease relative risks Introduction to Probability Events are possible outcomes of some random processes. Examples of events: – The genotype of a random individual is Bb – You pass 320 – the weight of a random individual is less than 150 pounds • We can define the probability of a particular event , say A, as the fraction of outcomes in which event A occurs. • Denote Probability of A by Pr(A), or Prob(A) Example: Flipping a coin • If you flip a coin once, the only possible outcome is a heads or a tails – Pr(Head) = 0.75 means that the chance is 75% that the outcome of a random flip is a head – Hence, Pr(Tail) = 1- Pr(head) = 0.25 – If you do 100,000 flips, you expect the number of heads to be around 75,000 (give or take). Probabilities can be counterintutive: Birthday problem

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Use rules of Probability • Rule 1: Pr(A) lies between 0 and 1 for all A – Probabilities are between zero (never occur) and one (always occur) • Rule 2: The sum of probabilities of all mutually exclusive (i.e., non-overlapping) events is one . – If there are n possible outcomes, Pr(1) + Pr(2) + … + Pr(n) = 1 – Hence, Pr(1) = 1 - [Pr(2) + … + Pr(n)] – KEY: Often easier to compute the probability of the COMPLETEMENT of an event to compute its probability AND and OR Rules AND rule : If A and B are independent events (knowledge of one event tells us nothing about the other event), then the probability that BOTH A and B occur is – Pr(A and B) = Pr(A) Pr(B) – Hence AND = multiply probabilities OR rule : If A and B are exclusive events (nonoverlapping), then the probability that EITHER A or B occurs is – Pr(A or B) = Pr(A) + Pr(B) – Hence OR = add probabilities Example: Suppose we are rolling a fair dice and flipping a fair coin • What is the probability of rolling an even
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1 Probability1 - Basic Probability Theory Genetics has a...

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