Question

Someone asked this question and I'm having a hard time answering it. Can someone point me in the right direction? Some kind of conditional probability? : What is the probability of "A" if P(AnB)=.20, P(AnC)=.16, and P(AnD)=.11 and we assume "A" can occur simultaneously with "B,C,D"

Answer 1

The last assumption doesn't help much… ("can" doesn't mean such element of A actually exists)
If A, B, C and D are stochastically independent i. e. \(P(X\cap Y)=P(X)\times P(Y) \forall X,Y\in \{A,B,C,D\}, X\neq Y\) then we could calculate \(P(A)=\frac{P(A\cap X)}{P(X)}\) With the given information alone, however, it's not possible to get a numerical value.

Answer 2

P(A)=P(AnB)+P(AnC)+P(AnD)=.47

Answer 3

Ah, you mean, A \(\textbf{only}\) occurs in B, C, or D, thus \(A\cap B^C\cap C^C\cap D^C=\emptyset \) (so P(A)=sum+P(∅)=47+0) !