Find $p$.

Find ${\text{E}}(X)$.

summing probabilities to 1     (M1)

eg,$\;\;\;\sum { = 1,{\text{ }}3 + 4 + 2 + x = 10}$

correct working     (A1)

$\frac{3}{{10}} + \frac{4}{{10}} + \frac{2}{{10}} + p = 1,{\text{ }}p = 1 - \frac{9}{{10}}$

$p = \frac{1}{{10}}$     A1     N3

[3 marks]

correct substitution into formula for ${\text{E}}(X)$     (A1)

eg$\;\;\;0\left( {\frac{3}{{10}}} \right) +  \ldots  + 3(p)$

correct working     (A1)

eg$\;\;\;\frac{4}{{10}} + \frac{4}{{10}} + \frac{3}{{10}}$

${\text{E}}(X) = \frac{{11}}{{10}}\;\;\;(1.1)$     A1     N2

[3 marks]

Total [6 marks]

Most candidates were able to find $p$, however expectation emerged as surprisingly more difficult. Quite often ${\text{E}}(X)/4$ was found or candidates wrote the formula with no further work.

Most candidates were able to find $p$, however expectation emerged as surprisingly more difficult. Quite often ${\text{E}}(X)/4$ was found or candidates wrote the formula with no further work.