A biased tetrahedral die has its faces marked with numbers $2$, $3$, $4$ and $5$. Let \

Question

A biased tetrahedral die has its faces marked with numbers $2$, $3$, $4$ and $5$. Let $X$ be the number on the face in contact with the table when the die is thrown. The probability of $X$ being $2$, $3$, $4$ and $5$ are $\frac{1}{10}$, $\alpha $, $\beta $ and $\frac{2}{5}$ respectively. A player throws the die and his score, $Y$, is given by $Y=\left| X-3 \right|$. Given that $\mathrm{Var}\left( Y \right)=0.56$, find the values of $\alpha $ and $\beta $.[6] Find the probability that a player’s mean score in $50$ throws is more than $1.3$.[2]

Accepted Answer

(i) $\alpha = \frac{1}{5}$, $\beta = \frac{3}{10}$ (ii) $0.172$

2022 TJC P2 Q7

2022 TJC P2 Q7

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