the value of p ;

\({\text{P}}(X = 10)\) ;

\({\text{P}}(X \geqslant 15)\) .

\({\text{E}}(X) = np\)

\( \Rightarrow 10 = 30p\)

\( \Rightarrow p = \frac{1}{3}\)     A1

[1 mark]

\(P(X = 10) = \left( {\begin{array}{*{20}{c}}
  {30} \\
  {10}
\end{array}} \right){\left( {\frac{1}{3}} \right)^{10}}{\left( {\frac{2}{3}} \right)^{20}} = 0.153\)     (M1)A1

[2 marks]

\({\text{P}}(X \geqslant 15) = 1 - {\text{P}}(X \leqslant 14)\)     (M1)

\( = 1 - 0.9565... = 0.0435\)     A1

[2 marks]

Again this proved to be an accessible question for students with many students gaining full marks. Most candidates used the calculator to find the answers to parts (b) and (c) which is what was intended, but candidates should be aware that there are often marks for recognising what needs to be found, even if the candidate does not obtain the final correct answer. It is suggested that in this style of question, candidates should indicate what they are trying to find as well as giving the final answer.

Again this proved to be an accessible question for students with many students gaining full marks. Most candidates used the calculator to find the answers to parts (b) and (c) which is what was intended, but candidates should be aware that there are often marks for recognising what needs to be found, even if the candidate does not obtain the final correct answer. It is suggested that in this style of question, candidates should indicate what they are trying to find as well as giving the final answer.

Again this proved to be an accessible question for students with many students gaining full marks. Most candidates used the calculator to find the answers to parts (b) and (c) which is what was intended, but candidates should be aware that there are often marks for recognising what needs to be found, even if the candidate does not obtain the final correct answer. It is suggested that in this style of question, candidates should indicate what they are trying to find as well as giving the final answer.