SPM.1.SL.TZ0.12

pestleMathematicsAISLPaper 1SPM· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

Jae Hee plays a game involving a biased six-sided die.

The faces of the die are labelled −3, −1, 0, 1, 2 and 5.

The score for the game, X, is the number which lands face up after the die is rolled.

The following table shows the probability distribution for X.

Jae Hee plays the game once.

Find the exact value of $p$ .

[1]

Calculate the expected score.

[2]

Jae Hee plays the game twice and adds the two scores together.

Find the probability Jae Hee has a total score of −3.

[3]

Markscheme / solution

$\frac{4}{{18}}\left( {\frac{2}{9}} \right)$ A1

[1 mark]

$- 3 \times \frac{1}{{18}} + \left( { - 1} \right) \times \frac{4}{{18}} + 0 \times \frac{3}{{18}} + \ldots + 5 \times \frac{7}{{18}}$ (M1)

Note: Award (M1) for their correct substitution into the formula for expected value.

$= 1.83\left( {\frac{{33}}{{18}}{\text{,}}\,1.83333 \ldots } \right)$ A1

[2 marks]

$2 \times \frac{1}{{18}} \times \frac{3}{{18}}$ (M1)(M1)

Note: Award (M1) for $\frac{1}{{18}} \times \frac{3}{{18}}$ , award (M1) for multiplying their product by 2.

$= \frac{1}{{54}}\left( {\frac{6}{{324}}{\text{,}}\,0.0185185 \ldots {\text{,}}\,1.85{\text{% }}} \right)$ A1

[3 marks]

Examiners’ report

[N/A]