If the odds in favour of an event are 3:5, what is the probability that the event occurs?

Introduction / Context:“Odds in favour” and “probability” are related but not identical. Converting between the two is a common basic skill in probability.

Given Data / Assumptions:

• Odds in favour = a:b means success : failure = a : b.
• Here a = 3, b = 5.

Concept / Approach:If odds in favour are a:b, then P(success) = a / (a + b) and P(failure) = b / (a + b).

Step-by-Step Solution:P = 3 / (3 + 5) = 3/8.

Verification / Alternative check:Corresponding odds against would be 5:3; then P = 1 / (1 + (5/3)) = 3/8, same result.

Why Other Options Are Wrong:3/5 uses only the “for” part; 1/3 and 1/5 are unrelated to 3:(something) totals.

Common Pitfalls:Confusing 3/5 with probability; odds are a ratio of counts, not a direct probability.

Final Answer:3/8