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:

If a number is chosen at random from the set $\{1, 2, 3, \ldots, 100\}$,then the probability that the chosen number is a perfect cube is

Three coins are tossed once. Let $A$ denote the event 'three heads show',$B$ denote the event 'two heads and one tail show',$C$ denote the event 'three tails show',and $D$ denote the event 'a head shows on the first coin'. Which events are mutually exclusive?

$A$ coin is tossed. If the outcome is a head,a die is thrown. If the die shows up an even number,the die is thrown again. What is the sample space for the experiment?

The probability of happening at least one of the events $A$ and $B$ is $0.6$. If the events $A$ and $B$ happen simultaneously with a probability of $0.2$,then $P(\bar{A}) + P(\bar{B}) = $

The vertices of a regular tetrahedron are marked $1, 2, 3, 4$. If three such tetrahedra are thrown simultaneously,what is the probability that the sum of the numbers on the faces is $5$?