Medium Practice — Set 2

Quick Recap — Probability Rules & Binomial

• Conditional: $P(A|B)=\dfrac{P(A\cap B)}{P(B)}$; independent $\Rightarrow P(A|B)=P(A)$.
• Bayes: $P(A|B)=\dfrac{P(B|A)P(A)}{P(B)}$.
• Binomial: $P(X=r)={}^nC_r\,p^rq^{n-r}$, with mean $np$ and variance $npq$.
• Odds in favour of $A$ $=\dfrac{P(A)}{P(A')}$.