Dice

We throw five times the dice. What is the probability that six fits exactly twice?

Result

p =  0.161

Solution:

$q=\dfrac{ 1 }{ 6 } \doteq 0.1667 \ \\ C_{{ 2}}(5)=\dbinom{ 5}{ 2}=\dfrac{ 5! }{ 2!(5-2)!}=\dfrac{ 5 \cdot 4 } { 2 \cdot 1 }=10 \ \\ \ \\ p=q^{ 2 } \cdot \ (1-q)^{ 5-2 } \cdot \ { { 5 } \choose 2 }=0.1667^{ 2 } \cdot \ (1-0.1667)^{ 5-2 } \cdot \ 10 \doteq \dfrac{ 625 }{ 3888 } \doteq 0.1608 \doteq 0.161$

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