17N.2.SL.TZ0.S_4

pestleMathematicsAISLPaper 217N· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

A discrete random variable $X$ has the following probability distribution.

N17/5/MATME/SP2/ENG/TZ0/04

Find the value of $k$ .

[4]

Write down ${\text{P}}(X = 2)$ .

[1]

Find ${\text{P}}(X = 2|X > 0)$ .

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

valid approach (M1)

eg $\,\,\,\,\,$ total probability = 1

correct equation (A1)

eg $\,\,\,\,\,$ $0.475 + 2{k^2} + \frac{k}{{10}} + 6{k^2} = 1,{\text{ }}8{k^2} + 0.1k - 0.525 = 0$

$k = 0.25$ A2 N3

[4 marks]

${\text{P}}(X = 2) = 0.025$ A1 N1

[1 mark]

valid approach for finding ${\text{P}}(X > 0)$ (M1)

eg $\,\,\,\,\,$ $1 - 0.475,{\text{ }}2({0.25^2}) + 0.025 + 6({0.25^2}),{\text{ }}1 - {\text{P}}(X = 0),{\text{ }}2{k^2} + \frac{k}{{10}} + 6{k^2}$

correct substitution into formula for conditional probability (A1)

eg $\,\,\,\,\,$ $\frac{{0.025}}{{1 - 0.475}},{\text{ }}\frac{{0.025}}{{0.525}}$

0.0476190

${\text{P}}(X = 2|X > 0) = \frac{1}{{21}}$ (exact), 0.0476 A1 N2

[3 marks]

Examiners’ report

[N/A]