A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true.

P(A1) = 0.12 P(A2) = 0.08 P(A3) = 0.05P(A1 U A2) = 0.14 P(A1 n A3) = 0.14P(A2 U A3) = 0.11 P(A1 n A2 n A3) = 0.01
(a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.)

The system of equations graphed below has how many solutions?

1. are the triangles similar and if so why? what is the value of x? show your work.

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."