If the odds against an event are 5:4, what is the probability that the event occurs?

Introduction / Context:
“Odds against” a:b means failure:success = a:b. We convert this ratio into a probability of success by dividing the success count by the total a + b.

Given Data / Assumptions:

• Odds against = 5:4.

Concept / Approach:
If odds against are a:b, then P(success) = b / (a + b). We simply plug in a = 5, b = 4.

Step-by-Step Solution:
P = 4 / (5 + 4) = 4/9.

Verification / Alternative check:
Corresponding odds in favour would be 4:5, giving P = 4/(4+5) = 4/9, consistent.

Why Other Options Are Wrong:
4/5 and 1/4 invert relationships; 1/5 uses only the “against” numerator as probability.

Common Pitfalls:
Confusing odds with probabilities; always divide by total a + b.

Final Answer:
4/9