How do you convert odds in favour or odds against into a probability?
Odds in favour a : b means a favourable outcomes for every b unfavourable, so the probability is a/(a + b). Odds against a : b mean probability b/(a + b). Odds in favour 3 : 5 give P = 3/8; odds against 7 : 3 give P = 3/10.
Explain it simply
Probability compares favourable cases with all cases. Odds compare favourable cases with unfavourable cases. So odds of 3 : 5 means 3 good outcomes against 5 bad ones, which is 8 outcomes in all. Probability is then 3 out of 8.
Example
Question 1: The odds in favour of India winning a match are 3 : 5. What is the probability India wins? P = 3 / (3 + 5) = 3/8.
Question 2: The odds against a student solving a puzzle are 7 : 3. What is the probability the student solves it? Odds against means unfavourable : favourable. P(solves) = 3 / (7 + 3) = 3/10.
Question 3: P(event) = 0.2. What are the odds in favour? 0.2 = 1/5, so 1 favourable to 4 unfavourable. Odds in favour = 1 : 4.
const fromOddsFor = (a, b) => a / (a + b);
console.log(fromOddsFor(3, 5)); // Output: 0.375
console.log(fromOddsFor(3, 7)); // Output: 0.3What to say in the interview
"Odds compare favourable to unfavourable, probability compares favourable to total. So odds in favour a to b gives a over a plus b, and odds against a to b gives b over a plus b."
Common mistakes
- Writing 3/5 as the probability for odds of 3 : 5.
- Reading odds against as odds in favour.