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

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:
${\displaystyle P(A\cap B\cap C\cap D)=P\left(A\right)\times P\left(B\right)\times P\left(C\right)\times P\left(D\right)}$
Then, the probability that at least one machine will be working is
P(At least one machine working)=1-P(None of them working)
${\displaystyle =1-P(A\cap B\cap C\cap D)}$
${\displaystyle =1-P\left(A\right)\times P\left(B\right)\times P\left(C\right)\times P\left(D\right)}$
${\displaystyle (\therefore \text{ Events are independent})}$
${\displaystyle =1-(0.04\times 0.01\times 0.06\times 0.01)}$
=1-0.00000024
=0.99999976
Thus, the probability that at least one machine will be working is 0.99999976 which is approximately 1