The probability that a turbine will have a defective coil is 0.10, the probability that it will have defective blades is 0.15, and the probability that it will have both defects is 0.04. (a) what is the probability that a turbine will have one of these defects? (b) what is the probability that a turbine will have neither of these defects?

When dealing with the union of two events, the formula states

You need to subtract elements belonging to both A and B, otherwise you would count them twice.

So, the probability that a turbine will have defective blades and defective coil is

To compute the probability of non-defective turbines, you can use this strategy: if we divide the sample space in subsets with no intersections, then they form a partition of the sample space, and you have

where is the sample space, and each is a subset of the partition.

In this case, we can use the following partition:

So, we have

And we are interest in , so we have

Now, the turbines with only defective coil are those with defective coils and non-defective turbines:

Similarly,

We already know , so we can solve