Q.The odds against student $X$ solving a statistics problem are 8:6 and odds in favour of student $Y$ solving the same problem are 14:16. Find the chance that i) the problem will be solved if they try it independently ii) neither of them solves 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.