# There are four washing machines in an apartment complex: A, B, C, D. On any given day the probability that these machines break down is as follows

There are four washing machines in an apartment complex: A, B, C, D. On any given day the probability that these machines break down is as follows:
P(A) = 0.04, P(B) = 0.01, P(C) = 0.06, P(D) = 0.01 .
Assume that the functionality of each machine is independent of that of others. What is the probability that on a given day at least one machine will be working?
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Anonym
Let A be first event that the washing machine not working, B be the second event that the washing machine not working, C be third event that the washing machine not working and D be fourth event that the washing machine not working.
From the given information, the P (4) = 0.04, P (B) =0.01, P (C) =0.06, P (D)=0.01 and all events are independent.
Step 2
Multiplication rule for independent events:
$P\left(A\cap B\cap C\cap D\right)=P\left(A\right)×P\left(B\right)×P\left(C\right)×P\left(D\right)$
Then, the probability that at least one machine will be working is
P(At least one machine working)=1-P(None of them working)
$=1-P\left(A\cap B\cap C\cap D\right)$
$=1-P\left(A\right)×P\left(B\right)×P\left(C\right)×P\left(D\right)$

$=1-\left(0.04×0.01×0.06×0.01\right)$
=1-0.00000024
=0.99999976
Thus, the probability that at least one machine will be working is 0.99999976 which is approximately 1
Jeffrey Jordon