Four identical dice are rolled once the probability that all the members on them are primes is 8 L + 2 L then L =

Question

Four identical dice are rolled once the probability that all the members on them are primes is 8 L + 2 L ​ then L =

TestHub · Accepted Answer

The total number of outcomes:

aaaa appear in $(1 6) = 6$ ways

aaab appear in $2 (2 6) = 30$ ways

$aabb$ appear in $(2 6) = 15$ ways

$aab c$ appear in $3 (3 6) = 60$ ways

abcd appear in $(4 6) = 15$ ways

Total $= 6 + 30 + 15 + 60 + 15 = 126$

The number of ways of primes appearing

aaaa appear in $(1 3) = 3$ ways

aaab appear in $2 (2 3) = 6$ ways

$aabb$ appear in $(2 3) = 3$ ways

aabc appear in $3 (3 3) = 3$ ways

Total $= 3 + 6 + 3 + 3 = 15$

Probability $= \frac{15}{126} = \frac{5}{42}$

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