Slide 1: Do you know…? What is a probability and what are odds?

Slide 2: Probability = # events of interest / # total possible events. Usually given as a percentage. Ranges from 1-100%. An example: If I select a patient below at random, what is the probability that I will select a purple one? [diagram with 2 orange, 5 yellow, 5 blue, 6 purple] purple / all colors = 6/18 = 1/3 = 33%. “The probability of selecting purple is thirty-three percent.”

Slide 3: Odds = # events of interest / # events NOT of interest. *not to be confused with “odds ratio” which is a specific application of odds used in measuring the association between two events. Usually given as a ratio of event TO not event. Ranges from 0 (very low) to infinity (very high). An example: If I select a patient below at random, what are the odds that I will select a purple one? [diagram with 2 orange, 5 yellow, 5 blue, 6 purple] purple / all other colors = 6:12 = 1:2 = 0.50. “The odds in favor of purple are one to two (or 0.50).”

Slide 4: What’s the point? To understand likelihood ratios (a future topic), you’ll need to understand the difference between these two concepts and that they are not interchangeable in equations.

Slide 5: You can, however, convert between the two. Probability of A = odds in favor of A / (1 + odds in favor of A). Odds of A = probability of A / 1 – probability of A. [diagram with 2 orange, 5 yellow, 5 blue, 6 purple] Probability of purple (from odds) = 0.5/1.5 = 1/3. Odds of purple (from probability) = 33%/67% = 1:2.

Slide 6: Takeaways. It’s not important to memorize these equations; rather, the takeaway points are that probability and odds are slightly different ways of representing an event occurrence, and you can convert from one to the other.