Probability

Probability theory is fundamental to the field of statistics. Here, we provide resources covering some key concepts, including probability distributions, adding and multiplying probabilities, conditional probabilities, and Bayes’ theorem.

 
Probability forms the foundation of statistics so we need to understand some basic principles of probability
 

Probability

How are poker and statistics similar? Well, they both rely on probability. Learn the basics of probability and you can ace your stats exam!

Additional Resources


Whitlock & Schluter - The Analysis of Biological Data

Chapter 5: pages 119-140 [Sapling]

 

Seeing Theory - Basic Probability

Intro: This website provides a visual and accessible overview of concepts related to probability.

 

Seeing Theory - Compound Probability

Intermediate: Visual representations and simulations of the probability of multiple events occurring.

 

Joint, marginal and conditional probabilities

Intermediate: Using probability tables to explain conditional probability.

Probability, Basic Overview

Intro: This video explains how to calculate the probability of an event occurring. It also discusses how to determine the sample space of an event using tree diagrams.

 

Conditional probability

Intermediate: What is the probability of an event A given that event B has occurred?

 

Bayes’ theorem

Advanced: When is it useful? Why is it true? What is it saying?


Review Questions

 
  1. Gregor Mendel (1822-1884) conducted experimental crosses with pea plants and recorded observations for multiple traits including pea color (yellow or green) and shape (round or wrinkled). When a parent plant with yellow, round peas was crossed with one with green, wrinkled peas, the F1-offspring all had peas that were yellow and round. However, when two F1s were crossed, the probability of an F2 having green peas was ¼, and the probably of an F2 having round peas was ¾. For the below questions, assume that the genes underlying pea color and roundness segregate independently.

    • What was the probability of observing an F2 plant with peas that were green and round?

    • What was the probability of observing an F2 plant with green peas or round peas?

    • If there were ten F2s, what was the probability that half were green and round, and the other half were yellow and wrinkled?

    • What is the probability of an F2 having green peas, given that it has wrinkled peas?

  2. Congenital night blindness is a genetic condition. If two heterozygous parents – which are ‘carriers’ for the condition – the probability of having an affected child is 0.25. What is the probability that two children born to a heterozygous couple BOTH have the condition, assuming independence?

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