John and Mary, are going to sit for an exam. The possible results that they can get are $A,B$ and $C$.
The possibility that John gets a $B$ is $0.3$. The possibility that Mary gets a $B$ is $0.4$.
The possibility that none of them gets an $A$, but at least one of them get a $B$ is $0.1$. What is the possibility that at least one of them gets a $B$, but none of them gets a $C$ ? .
So far, my approach is like:
For John get a B: $P(J_B)=0.3$
For Mary get a B: $P(M_B)=0.4$
Also, As given in the question, [P(John_B) \cup P(Mary_B) ] ∩ P(A') = 0.1
And I am trying to find
[P(John_B) ∪ P(Mary_B)] ∩ P(C')
To begin with, are my assumptions so far good/sufficient ?