The random variable $X$ is the number of successes in $n$ independent trials of an experiment in which the probability of a success at any trial is $p$.
Denoting $\mathrm{P}\left( X=k \right)$ by ${{p}_{k}}$, it is given that $\frac{{{p}_{k}}}{{{p}_{k-1}}}=\frac{\left( n-k+1 \right)p}{k\left( 1-p \right)},k=1,2,...,n$.
A distribution is said to be bimodal if it has two modes.
Find the least value of $n$, and the corresponding modes of $X$, given that $X$ is bimodal and that $p=\frac{18}{25}$.[3]

The random variable $X$ is the number of successes in $n$ independent trials of an experiment in which the probability of a success at any trial is $p$.

Denoting $\mathrm{P}\left( X=k \right)$ by ${{p}_{k}}$, it is given that $\frac{{{p}_{k}}}{{{p}_{k-1}}}=\frac{\left( n-k+1 \right)p}{k\left( 1-p \right)},k=1,2,...,n$.

A distribution is said to be bimodal if it has two modes.

Find the least value of $n$, and the corresponding modes of $X$, given that $X$ is bimodal and that $p=\frac{18}{25}$.

2017 ACJC MYE P2 Q8

2017 ACJC MYE P2 Q8

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