Probability
(only works for Bernoulli distribution e.g. true or false)

Odds

both are different ways to numerically represent uncertainty. Uncertainty can also be represented in Odds Ratio

𝐏(𝑋)

𝐎(𝑋)

the number of ways that an outcome can occur+the number of ways it cannot occur = the whole number of cases possible

the ratio of the number of ways that an outcome can occur compared to the whole number of cases possible

probability=the number of ways that an outcome can occur /the whole number of cases possible

probability = odds / (1 + odds)

the ratio of the number of ways that an outcome can occur compared tothe number of ways it cannot occur

odds =the number of ways that an outcome can occur /the number of ways it cannot occur

odds = probability / (1 - probability)

1/5 = 𝐏(𝑋)𝐎(𝑋) = 1/41:4 = Odds Ratio

ranges between an interval of [0,1]

ranges between an interval between [0, infinity)

Relation Between Probability and Odds

  • odds = probability / (1 - probability)
  • odds(1 - probability) = probability
  • odds - odds*probability = probability
  • odds = probability + odds*probability
  • odds = probability (1 + odds)
  • odds/(1 + odds) = probability