The probability of obtaining an even prime number on each die,when a pair of dice is rolled,is . . . . . . .

Let $A$ and $B$ be events for which $P(A) = x$,$P(B) = y$,and $P(A \cap B) = z$. Then $P(\bar{A} \cap B)$ equals:

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$,then the probability of both of them occurring together is

Suppose $A$ and $B$ are two events such that $P(A) = 0.9$,$P(B) = 0.8$,and $P(A \cap B) \geq 0.7$. Then,we can conclude that such a case is . . . . . .

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

For two events $A$ and $B$,if $P(A \cup B) = \frac{5}{6}$,$P(A) = \frac{1}{6}$,and $P(B) = \frac{2}{3}$,then $A$ and $B$ are: