2．The discrete random variable \(X\) follows the binomial distribution $$X \sim \mathrm {~B} ( n , p )$$ where \(0 < p < 1\) ．The mode of \(X\) is \(m\) ．
（a）Write down，in terms of \(m , n\) and \(p\) ，an expression for \(\mathrm { P } ( X = m )\)
（b）Determine，in terms of \(n\) and \(p\) ，an interval of width 1 ，in which \(m\) lies．
（c）Find a value of \(n\) where \(n > 100\) ，and a value of \(p\) where \(p < 0.2\) ，for which \(X\) has two modes． For your chosen values of \(n\) and \(p\) ，state these two modes．