What is wrong with these probability assignments.

Question

Greg is setting a question for quiz.He assigns these probabilities P(A) = .6, P(B) is .7 P(A|B) = .1 and asks for P(A or B).What is wrong with these probability assignments.

Answer 1

Make a Venn diagram with circles A and B overlapping partially.

There will be three distinct areas enclosed by arcs; label their contents (probabilities) as a, b & c, from left to right, with P(A) = a+b, = .6 P(B) = b+c = .7 and b representing P(A|B) = .1

 

Therefore a=.5 and c=.6 using algebra (substituting for b)

 

Then the sum a+b+c represents P(A ∪ B) which is .5 + .1 + .6 or 1.2 which is impossible (exceeds 1.0).