Q.The odds against an event are 5:3 and the odds in favour of another independent event are 7:5. The probability that at least one of the two events will occur is A) $\frac{52}{96}$ B) $\frac{71}{96}$ C) $\frac{69}{96}$ D) $\frac{13}{96}$

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 …