given the probabilities: P(A & B^c) = 0.15 , P(A^c & B)= 0.30 , and P(A^c & B^) = 0.35 find P(B)

Question

given the probabilities: P(A & B^c) = 0.15 , P(A^c & B)= 0.30  , and P(A^c & B^) = 0.35 find P(B)

amistre64 · Answer

i havent come across an '^' in probablitites yet; whats it mean?

anonymous · Answer

I can't figure out how to make a small C at the top for compliment... so I tried that...

amistre64 · Answer

ohh; compliment :)

anonymous · Answer

Yeah :) Sorry if it was confusing!

amistre64 · Answer

-A is the complement of A right?

anonymous · Answer

I think so

amistre64 · Answer

$$\bar A$$ in latex :)

amistre64 · Answer

it looks tricky; but a venn diagram might be helpful

anonymous · Answer

i get .45

anonymous · Answer

The right answer is .5 but I don't know how to get it

anonymous · Answer

really? let me try again

anonymous · Answer

yeah would help if i knew how to add!

anonymous · Answer

easiest way is to draw a venn diagram. you have everything known but 
$$P(A\cap B)$$ and so add up, subtract from 1 and get 
$$P(A\cap B)=.2$$

anonymous · Answer

it is .5

anonymous · Answer

.3+(1-(.15+.35+.3))=.5

anonymous · Answer

since 
$$P(B)=P(A\cap B) + P(A^c \cap B)$$ you get it

anonymous · Answer

would you like to see the venn diagram or are you happy with the answer?

anonymous · Answer

Happy with the answer, thank you!