Question

A uniform unbised die is constructed in the shape of a regular tetrahedron with faces numbered $2,2,3$ and $4$ and the score is taken from the face on which the die lands. If two such dice are thrown together, find the probability of scoring.
(i). exactly $6$ on each of $3$ successive throws
(ii) more than $4$ on at least one of the three successive throws.

Answer 1

$n\left(s\right)=$total no of outcomes $=4\times 4=16$

$n(sumofnumbers=6)=5[(2,4),(2^{\prime },4),(4,2)(4,2^{\prime }),(3,3)]$

$p$(exactly $6$ one each successive $3$ throws)$=\frac{5}{16}\times \frac{5}{16}\times \frac{5}{16}\times =\frac{125}{4096}$

$p$(exactly $6$ one each succ $3$ throws) $=1-p\left(4on3throws\right)$

$=1-\frac{4}{16}\times \frac{4}{16}\times \frac{4}{16}\times =\frac{63}{64}$