Find the value of r .

Given that ${\rm{E}}(X) = 1.4$ , find the value of p and of q .

attempt to substitute ${\rm{P}}(X > 1) = 0.5$     (M1)

e.g. $r + 0.2 = 0.5$

$r = 0.3$     A1     N2

[2 marks]

correct substitution into ${\rm{E}}(X)$ (seen anywhere)     (A1)

e.g. $0 \times p + 1 \times q + 2 \times r + 3 \times 0.2$

correct equation     A1

e.g. $q + 2 \times 0.3 + 3 \times 0.2 = 1.4$ , $q + 1.2 = 1.4$

$q = 0.2$     A1      N1

evidence of choosing $\sum {{p_i} = 1}$     M1

e.g. $p + 0.2 + 0.3 + 0.2 = 1$ , $p + q = 0.5$

correct working     (A1)

$p + 0.7 = 1$ , $1 - 0.2 - 0.3 - 0.2$ , $p + 0.2 = 0.5$

$p = 0.3$     A1 N2

Note: Exception to the FT rule. Award FT marks on an incorrect value of q, even if q is an inappropriate value. Do not award the final A mark for an inappropriate value of p.

[6 marks]

The majority of candidates were successful in earning full marks on this question.

In part (b), a small number of candidates did not use the correct formula for ${\rm{E}}(X)$ , even though this formula is given in the formula booklet. There were also a few candidates who incorrectly assumed that $p = 0$ , forgetting that the sum of the probabilities must equal 1. There were a few candidates who left this question blank, which raises concerns about whether they had been exposed to probability distributions during the course.