There are two kinds of tubes in an electronic gadget. It will cease to function if and only if one of each kind is defective. The probability that there is a defective tube of the first kind is .1; the probability that there is a defective tube of the second kind is .2. It is known that two tubes are defective, what is the probability that the gadget still works?
If there are only two kinds of tubes and the probability that a defective tube is of type A is 0.1 then shouldn't it follow that the probability that a defective tube belongs to type B is 0.9 as a defective tube can either be of type A or type B?
Isn't the question kind of wrong?