18M.1.AHL.TZ1.H_3

pestleMathematicsAIHLPaper 118M· sl-4-7-discrete-random-variablessource ↗

Two unbiased tetrahedral (four-sided) dice with faces labelled 1, 2, 3, 4 are thrown and the scores recorded. Let the random variable T be the maximum of these two scores.

The probability distribution of T is given in the following table.

Find the value of a and the value of b.

[3]

Find the expected value of T.

[2]

Markscheme / solution

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

$a = \frac{3}{{16}}$ and $b = \frac{5}{{16}}$ (M1)A1A1

[3 marks]

Note: Award M1 for consideration of the possible outcomes when rolling the two dice.

${\text{E}}\left( T \right) = \frac{{1 + 6 + 15 + 28}}{{16}} = \frac{{25}}{8}\left( { = 3.125} \right)$ (M1)A1

Note: Allow follow through from part (a) even if probabilities do not add up to 1.

[2 marks]

Examiners’ report

[N/A]