If $A$ and $B$ are two events such that $P(A | B) = 0.6$, $P(B | A) = 0.3$, and $P(A) = 0.1$, then $P(\bar{A} \cap \bar{B})$ equals:

If $E$ and $F$ are two independent events with $P(E)=0.3$ and $P(E \cup F)=0.5$, then $P(E|F)-P(F|E)$ equals

$A$ die is thrown. If $E$ is the event 'the number appearing is a multiple of $3$' and $F$ is the event 'the number appearing is even',then find whether $E$ and $F$ are independent?

If $A$ and $B$ are two independent events such that $P(B)=\frac{2}{7}$ and $P(A \cup B^c)=0.8$,then $P(A)$ is equal to:

$A$ and $B$ are two events such that $P(A) = 0.8$,$P(B) = 0.6$,and $P(A \cap B) = 0.5$. Then the value of $P(A/B)$ is:

If $P(AB) = P(A)P(B)$,$P(A/B) = 1/4$,and $P(B/A) = 1/3$,then which of the following is true?