Question

let A and B be events such that Pr (A U B)= .9 and Pr [A ]=.5. What is Pr [B] in the following case that A and B are independent?

Answer 1

if they are independent than Pr (A U B)= Pr [A +Pr [B]

hope ts helps

Answer 2

this is wrong sorry, got mixed up had a feeling that this is the case

Answer 3

P(A) + P(B) - P(AnB) = P(AuB)

plus if they are independent than P(AnB) = P(A)P(B) .

Answer 4

so in this case
0.9=0.5+P(B)-P(AnB)=0.5+P(B)-0.5P(B)

Answer 5

solving this gives P(B)=0.8

Answer 6

thanks also another question.. does [(E U F)'] = E' U F' or does it intersect

Answer 7

For the first one you might find it easier to do: \[P (A \cup B) = P(A) - P\left(\begin{matrix}B \\A\end{matrix}\right)\]
which gives \[0.9 = 0.5 + \left(\begin{matrix}B \\0.5\end{matrix}\right)\]

Answer 8

(EUF)' = E' (intersection) F'