Question 1130880
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Missing parts on the given diagram:<br>
(1) P(B) = 1-(1/4+1/3) = 5/12
(2) P(Dc|A) = 1-1/3 = 2/3
(3) P(D|B) = 1-1/5 = 4/5
(4) P(D|C) = 1-1/6 = 5/6<br>
Answers to the questions:<br>
(a) P(D) = (1/4)(1/3)+(5/12)(4/5)+(1/3)(5/6) = 1/12+1/3+5/18 = (3+12+10)/36 = 25/36<br>
(b) P(B|D) = [P(B and D)]/P(D) = (1/3)/(25/36) = (12/36)/(25/36) = 12/25<br>
(c) P(Dc) = 1-P(D) = 11/36  (or P(Dc) = (1/4)(2/3)+(5/12)(1/5)+(1/3)(1/6) = 1/6+1/12+1/18 = (6+3+2)/36 = 11/36)<br>
(d) P(A|Dc) = [P(A and Dc)]/P(Dc) = (1/6)/(11/36) = (6/36)/(11/36) = 6/11<br>