Pr radar detecting an aircraft

Hi All,

I think I have the right answer for this, but I'm not that confident on these questions..

Three radar sets, operating independently, are set to tdetect any aircraft flying through a certain area. Each set has a probability of .02 of failing to detect a plane in its area. If an aircraft enters the area, what is the probability that it

**a** goes undeteected?

**b** is detected by all three radar sets?

So I defined the events;

- first fails

- second fails

- third fails.

Then

With

and

So

And **b** detected by all three;

Thanks for any help