Is an answer possible - Conditional Probability

[Manasan3010]

Homework Statement

p(a)=0.75
p(b|a)=0.9
p(b|a')=0.8
p(c|a'b)=0.7
p(c|a'b')=0.3
p(c|ab')=0.6
(These are the only data I was given)
Find p(abc)?

Relevant Equations

p(abc) = p(a)p(b|a)p(c|ab)

I am a noob to this topic so correct me If I made any silly mistake. By plugging in the values I managed to get

p(abc)=0.75*0.9*p(c|ab)
Here How can I find p(c|ab)? Is this question unsolvable or can I derive it?
I also want to know what is meant by p(abc) in literary terms.

I also created a Tree Diagram for the question(Correct me if there is any mistake)

 

[lewando]

Your tree looks right.

I think you don't have enough information in the problem statement to produce an singular answer. You could provide a range of probabilities, though.

"p(abc)" = P(a, b, c) = is a notation for the probability of a and b and c happening.

 

[Manasan3010]

I think you don't have enough information in the problem statement to produce an singular answer. You could provide a range of probabilities, though.

"p(abc)" = P(a, b, c) = is a notation for the probability of a and b and c happening.

How can I get a range of probabilities? (My guess is From 0 to 0.675, How can I represent this range Symbolically?)
How can I represent the above tree chart in a venn diagram?
Are there any difference between p(abc), p(a and b and c), p(a∩b∩c )

THANK YOU

 

[lewando]

How can I get a range of probabilities? (My guess is From 0 to 0.675, How can I represent this range Symbolically?)

Your guess is right, but why guess? You should be able to rationalize this.
How about: 0.675 >= p(abc) >= 0

How can I represent the above tree chart in a venn diagram?

Have you tried researching "3-event Venn diagrams"? There are plenty of examples (3 overlapping circles in a rectangular sample space) "out there". The sample space will consist of 8 non-overlapping regions. These correspond to the 8 "endpoints" of your tree.

Are there any difference between p(abc), p(a and b and c), p(a∩b∩c )

No.