Find the value of $k$.

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

evidence of using $\sum {{p_i}}  = 1$     (M1)

correct substitution     A1

eg$\;\;\;0.15 + k + 0.1 + 2k = 1,{\text{ }}3k + 0.25 = 1$

$k = 0.25$     A1     N2

[3 marks]

correct substitution     (A1)

eg$\;\;\;0 \times 0.15 + 1 \times 0.25 + 2 \times 0.1 + 3 \times 0.5$

${\text{E}}(X) = 1.95$     A1     N2

[2 marks]

Total [5 marks]