SOLUTION: Here's a website with a picture of the diagram: https://www.webassign.net/waplots/8/5/80b6596002a9fb8c3909017f691f1c.gif The accompanying diagram represents a two-stage experim

Algebra ->  Finance -> SOLUTION: Here's a website with a picture of the diagram: https://www.webassign.net/waplots/8/5/80b6596002a9fb8c3909017f691f1c.gif The accompanying diagram represents a two-stage experim      Log On


   



Question 1130880: Here's a website with a picture of the diagram: https://www.webassign.net/waplots/8/5/80b6596002a9fb8c3909017f691f1c.gif
The accompanying diagram represents a two-stage experiment. Here,
B = (A ∪ C)c.
Complete the information on the diagram, and use it to find the following.
a) P(D)
b) P(B | D)
c) P(Dc)
d) P(A | Dc)

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Missing parts on the given diagram:

(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

Answers to the questions:

(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

(b) P(B|D) = [P(B and D)]/P(D) = (1/3)/(25/36) = (12/36)/(25/36) = 12/25

(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)

(d) P(A|Dc) = [P(A and Dc)]/P(Dc) = (1/6)/(11/36) = (6/36)/(11/36) = 6/11