A polling company reports that there is a 20% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?  Choices:
A) 10	B) 8	C) 6	D) 4	E) 5
20% - Candidate Elected   100%-60% = 40% - Candidate doesnotsigh Bill X   50% - Candidate randomly chooses between two bills.   These are multiplicative:   20% x 40% x 50%   0.2 x 0.4 x 0.5 100 -60= 
<gadget id="calculator">100 -60</gadget>
<output>40</output>
40% - Candidate doesnotsigh Bill X   50% - Candidate randomly chooses between two bills.   These are multiplicative:   20% x 40% x 50%   0.2 x 0.4 x 0.5= 0.04 = 4%   Answer (4)
<result>D</result>
A polling company reports that there is a 20% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?