An unbiased die has three faces painted red, two faces painted green and one face painted blue. A re

Question

An unbiased die has three faces painted red, two faces painted green and one face painted blue. A red face has a score of $1$ point, a green face has a score of $2$ points and a blue face has a score of $3$ points.

Two such dice are thrown and the sum of their scores is denoted by $X$.

Show that $\mathrm{P}\left( X=4 \right)=\frac{5}{18}$ and find the probability distribution of $X$.[3]
Find $\mathrm{E}\left( X \right)$ and show that $\mathrm{Var}\left( X \right)=\frac{10}{9}$.[2]

Suppose now a red face has a score of $3$ points, a green face has a score of $2$ points and a blue face has a score of $1$ point.

Deduce the expectation and variance of the sum of scores obtained from a throw of two such dice.[2]

Accepted Answer

(ii) $\mathrm{E}(X) = \dfrac{10}{3}$; (iii) $\mathrm{E}(Y) = \dfrac{14}{3}$, $\mathrm{Var}(Y) = \dfrac{10}{9}$

2018 TMJC P2 Q5

2018 TMJC P2 Q5

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