Andrew plays 10 tennis matches. In each match he either wins or loses.
(a) State, in this context, two conditions needed for a binomial distribution to arise.
(b) Assuming these conditions are satisfied, define a variable in this context which has a binomial distribution.
The random variable \(X\) has the distribution \(\mathrm { B } ( 21 , p )\), where \(0 < p < 1\).
Given that \(\mathrm { P } ( X = 10 ) = \mathrm { P } ( X = 9 )\), find the value of \(p\).