| Date | May 2018 | Marks available | 3 | Reference code | 18M.1.hl.TZ1.3 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
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]
a.
Find the expected value of T.
[2]
b.
Markscheme
\(a = \frac{3}{{16}}\) and \(b = \frac{5}{{16}}\) (M1)A1A1
[3 marks]
Note: Award M1 for consideration of the possible outcomes when rolling the two dice.
a.
\({\text{E}}\left( T \right) = \frac{{1 + 6 + 15 + 28}}{{16}} = \frac{{25}}{8}\left( { = 3.125} \right)\) (M1)A1
Note: Allow follow through from part (a) even if probabilities do not add up to 1.
[2 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 5 - Core: Statistics and probability » 5.5 » Concept of discrete and continuous random variables and their probability distributions.
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