The event of the machine working is [tex]A\cap B\cap C\cap D[/tex], and since the components operate independently, we have
[tex]P(A\cap B\cap C\cap D)=P(A)P(B)P(C)P(D)[/tex]
so just multiply the given probabilities together,
[tex]P(A\cap B\cap C\cap D)=0.99^2\cdot0.94\cdot0.93\approx0.8568[/tex]
