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

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) (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

RELATED QUESTIONS
Find the length of side x. Round to the nearest tenth.... (answered by mananth)

Find the length of side x. Round to the nearest tenth.... (answered by math_tutor2020)

Find the area of the sector. Round to two decimal places.... (answered by mananth)

Determine the amplitude, period, midline, and an equation involving the cosine for the... (answered by MathLover1)

Find an equation for f(x) using the cosecant function.... (answered by Theo,MathLover1,ikleyn)

Find the measure of each angle in the triangle shown in the figure below. Round to the... (answered by MathLover1,math_tutor2020)

Find the area of the triangle. Round your answer to the nearest tenth.... (answered by MathLover1,ikleyn)

Find the area of the triangle. Round your answer to the nearest tenth.... (answered by mananth)

Find the measure of angle x, if possible. Notice that x is an obtuse angle. Round to the... (answered by mccravyedwin,MathLover1,ikleyn)