# Solved (Free): The probability that first processing machine is not working properly at any time is 0.07

#### ByDr. Raju Chaudhari

Apr 12, 2021

The probability that first processing machine is not working properly at any time is 0.07, and the probability that the second machine is not working properly at any time is 0.07 and the probability that third machine is not working properly is 0.09.

Find the probability that at least one machine will be working properly at any given time. Provide answer to four decimal precision

#### Solution

Let $A$ be the event that first processing machine is not working properly at any time.

Let $B$ be the event that second processing machine is not working properly at any time.

Let $C$ be the event that third processing machine is not working properly at any time.

Given that $P(A) = 0.07$, $P(B)=0.07$ and $P(C) = 0.09$.

Let $E$ be the event that at least one machine will be working properly at any given time.

Then the probability that at least one machine will be working properly at any given time is

 \begin{aligned} P(E) & = 1- P(\text{no machine working properly})\\ & = 1- P(A\cap B\cap C)\\ &\quad \quad \text{( A, B, C are independent)}\\ &= 1- P(A)P(B)P(C)\\ &= 1- (0.07)*(0.07)*(0.09)\\ &= 1- 0.000441\\ &= 0.999559 \end{aligned}