A biased $6$-sided die gives the score $1$, $2$, $3$, $4$, $5$, and $8$ with probabili

Question

A biased $6$-sided die gives the score $1$, $2$, $3$, $4$, $5$, and $8$ with probabilities shown in the table below, where $p$ and $q$ are positive constants such that $p\ne q$. Score$1$$2$$3$$4$$5$$8$ Probability$p$$q$$0.1$$p - q$$0.2$$p + q$ Explain why a score of $1$ is more likely to happen than a score of $2$.[1] Show that $3p+q=0.7$.[1] Given that the mean score is $4$, $6$, find the variance of the score.[5]

Accepted Answer

(i) $p>q$ (ii) $3p+q=0.7$ (iii) $p=0.18$, $q=0.16$, $\mathrm{Var}(X)=7.64$

2024 MI P2 Q7

2024 MI P2 Q7

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