CFA Practice Question
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CFA Practice Question
For the tree diagram shown below:
P(not B | A) = ______
Correct Answer: C
From the tree diagram, we know that 0.3 times P(B | A) = 0.2. Now, 0.3x = 0.2 yields x = 0.2/0.3 = 2/3. Thus, P(B | A) = 2/3. We have: P(B | A) + P(not B | A) = 1. Finally, 2/3 + P(not B | A) = 1 and P(not B | A) = 1 - 2/3 = 1/3.
User Contributed Comments 17
|stevelaz||Can someone explain this?|
|BayAreaPablo||I agree how can P(B|A) go from .2 to .67?|
|BayAreaPablo||I get it:
Now that you have this:Remember
P(B|A) + P(not B|A)=1
Now solve for P(not B|A)
|surob||I don't still understand why 0.2 = P(AB)?|
|cp24||What's misleading is that probability 0.2 is not P(B/A) but P(BA).|
|epizi||I don't think there is any problem,because the tree indicates that A happens before B, not both happening same time.Therefore P(A)=0.3 and P(B)=?
But the P(AB)=0.2
P(B/A) and P(notB/A) are exhaustive ie sum up to 1
So 1-P(B/A)=P(not B/A)
Hence 1-2/3= 1/3
Hope this makes it clear, I did not get it from first try either
|StanleyMo||thanks epizi. nice explain.|
|JKiro||I find this a bit more clearer...
what we know:
p(A) * p(B|A) = 0.2; we also know p(A) = 0.3
solving for p(B|A): 0.2/0.3 = 0.6667
what we also know:
p(B|A) + p(not B|A) must equal 1
we have calculated p(B|A)
solving for p(not B|A): 1 - 0.6667 = 0.3333
|fedha||JKiro I am not sure how you know p(B|A)is 0.2??
I hope you meant p(BA)= 0.2
Here is how would solve this problem. Epizi is right in solving the problem
P(B|A) = P(BA)/P(A)
P(B|A) = 0.2/0.3
P((B|A) = 0.667
We know that P(B|A) + P(Not B|A) = 1
We already solved for P(B|A) = 0.0667 Therefore
P(Not B|A) = 1-0.667 = 0.333 ~ 1/3
|loisliu88||I don't understand how can P(B/A)+P(notB/A)=1, what about P(notA). shouldn't it be P(B/A)+P(notB/A)+P(notA/B)+P(notA/notB)=1? plz explain it to me.|
|harpalani||Good explanation epizi!!|
|LordRommel||Oh. It is simple. 0.01/0.03 = 1/3|
|Saxonomy||If I understood the diagram, the answer would be easy.
Loisliu88, too much going on in your comment:
P(B|A) + P(notB|A) = 1
Ignore the "|A", just know that B + "notB" will always be 1.
Prob that LeBron wins the title (given the fact that the Lakers/Celtics are out) + the prob that LeBron does not win the title (given the fact that the Lakers/Celtics are out) equals 1.
|2014||Good explnation Fedha|
|sgossett86||CFAs, this problem upset me. Like they say above, turns out I wasn't reading the chart right.
|Scc0813||Why is 0.2 P(AB) and not P(B|A)?|
|Safiya921||I didn't read the Tree Diagram correct. I thought P(B I A) = 0.2, then I got to know from your comments that it's P (AB) = 0.2.
Thank you all.