Please explain each step and write clear Ignore the black do

Please explain each step and write clear. Ignore the black dots.

4. Consider the following system with the assigned probabilities of malfunction for the five components. Assuming that malfunctions occur independently, what is the system does not malfunction?

Solution

P(system does not malfunction) = 1 - P(system malfunctions)

P(system malfunctions) = 0.3*P(top half malfunctions)

P(top half malfunctions) = P(top left half malfunctions) + P(top right half malfunctions) - P(both top left and right halfs malfunctions)

= (0.2)*(0.1) + (0.1)*(0.3) - (0.2)*(0.1)*(0.1)*(0.3)

= 0.0494

So P(system malfunctions) = 0.3*P(top half malfunctions) = 0.3*0.0494 = 0.01482

So P(system does not malfunction) = 1 - P(system malfunctions) = 1 - 0.01482 = 0.98518