In a workshop, there are five machines and the probability of any one of them to be out of…

Question

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $${{1 \over 4}}$$
. If the probability that at most two machines will be out of service on the same day is $${\left( {{3 \over 4}} \right)^3}k$$, then k is equal to :

Accepted Answer

Probablity of at most two machines will be out of service = $${\left( {{3 \over 4}} \right)^3}k$$

$$ \Rightarrow $$ 5C0$${\left( {{3 \over 4}} \right)^5}$$ + 5C1$$\left( {{1 \over 4}} \right){\left( {{3 \over 4}} \right)^5}$$ + 5C2$${\left( {{1 \over 4}} \right)^2}{\left( {{3 \over 4}} \right)^5}$$ = $${\left( {{3 \over 4}} \right)^3}k$$

$$ \Rightarrow $$ $${{17} \over 8}{\left( {{3 \over 4}} \right)^3}$$ = $${\left( {{3 \over 4}} \right)^3}k$$

$$ \Rightarrow $$ k = $${{17} \over 8}$$

Solutions · 1