Question

Can anyone provide me with some guidance on this problem? What is P(ABC) if P(a)=P(B)=P( C)=.5, P(AUB)=.55, P(AUC)=.7, P(BC)=.3, and P(ABC)=2P(ABC^(complement))?

Answer 1

i have tried calculating some of the other things as well but I dont think they got me any closer to an answer. I also know the answer should be .3 but i dont understand how to get to that

Answer 2

hmm, auc = a + c - ac
aub = a + b - ab
bc = b (c|b)


hmm

Answer 3

ya i found P(ab) to be .45 and P(AC) to be .3

Answer 4

auc = a + c - ac = .7
aub = a + b - ab = .55

and a=b=c=.5

auc = .5 + .5 - ac = .7
aub = .5 + .5 - ab = .55

Answer 5

using the first two you said

Answer 6

ac = .3
ab = .45

Answer 7

bc = .5 (c|b) = .3

c|b = 3/5

Answer 8

i also know my professor said that this may be useful:
P(AUBUC) = P(A)+P(B)+P(C)-P(AB)-P(AC)-P(BC)+P(ABC)