Question

How to identify whether the quetion follow binomial expansion pattern or distribution pattern?

Answer 1

We use Binomial Expansion to expand a binomial expression (which is nothing but an algebraic expression involving only 2 terms) when it has been raised to some positive integral power (generally when it is inconveniently large). It can be formally expressed as:-

${\left(a+b\right)}^n=\sum _{k=0}^n{}^{n}C_k{a}^{n-k}{b}^k$

where $$\begin{gathered} aandb\to the2algebraicterms \\ n,k\in N \end{gathered}$$

We use Binomial Distribution to find the probability of occurence of Bernoulli Trials (which are independent trials that have only 2 outcomes, like yes/no, true/false, success/failure, etc.). It can be formally stated as:-

$P\left(x\right)={}^{n}C_x{P}^x{\left(1-P\right)}^{n-x}$

where $$\begin{gathered} x\to theindependentevent \\ n\to numberoftrials \end{gathered}$$