Let $S$ be the sample space of a random experiment and $P$ be a probability function defined on the power set of $S$. Two events $A$ and $B$ of the random experiment are called independent if

An ordinary cube has four blank faces,one face marked $2$,and another marked $3$. The probability of obtaining a total of exactly $12$ in $5$ throws is:

The probabilities that players $A$ and $B$ of a team are selected for the captaincy for a tournament are $0.6$ and $0.4$, respectively. If $A$ is selected as the captain, the probability that the team wins the tournament is $0.8$ and if $B$ is selected as the captain, the probability that the team wins the tournament is $0.7$. Then the probability, that the team wins the tournament, is:

One die has two faces marked $1$,two faces marked $2$,one face marked $3$ and one face marked $4$. Another die has one face marked $1$,two faces marked $2$,two faces marked $3$ and one face marked $4$. The probability of getting the sum of numbers to be $4$ or $5$,when both the dice are thrown together,is

$A$ and $B$ are independent events with $P(A)=\frac{1}{4}$ and $P(A \cup B)=2 P(B)-P(A)$,then $P(B)$ is

There are four fair dice $D_1, D_2, D_3$ and $D_4$. Each has six faces numbered $1, 2, 3, 4, 5$ and $6$. They are rolled one by one. What is the probability that the number shown on $D_4$ is equal to at least one of the numbers shown on $D_1, D_2$ and $D_3$ (in $/216$)?