Q.If odds in favour of $X$ solving a problem are 4:3 and odds against $Y$ solving the same problem are 2:3. Find probability of: i) $X$ solving the problem ii) $Y$ solving the problem.

Odds express the same information as probability but as a ratio of favourable to unfavourable outcomes rather than a fraction of the total. If $m$ of $n$ equally likely outcomes favour event $A$, the odds in favour of $A$ are $m:(n-m)$, equivalently $P(A):P(A')$; the odds against $A$ are the reverse ratio $(n-m):m$, equivalently $P(A'):P(A)$. Given odds in one form, the corresponding probability is recovered as (favourable count)/(favourable + unfavourable count); conversely, given a probability, the odds follow by taking the ratio of $P(A)$ to $P(A')$. Odds are commonly stated in real-world problems (insurance, games, sport) in place of raw probabilities, so converting cleanly between the two forms is an essential skill.