A polling company reports that there is a 80% 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?
Pick.
A) 10 B) 16 C) 6 D) 4 E) 5
80% - Candidate Elected   100%-60% = 40% - Candidate doesnotsigh Bill X   50% - Candidate randomly chooses between two bills.   These are multiplicative:   80% x 40% x 50%   0.8 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:   80% x 40% x 50%   0.8 x 0.4 x 0.5= 0.16 = 16%   Answer (16)
<result>B</result>
A polling company reports that there is a 80% 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?