Two dice are thrown simultaneously. If $A$ is the event of getting the sum of the numbers on two dice as greater than or equal to $8$ and $B$ is the event of getting a number less than or equal to $3$ on at least one of the dice. Then,$P(B / A) = $

Find $P(E | F)$ for a coin tossed three times,where $E:$ at most two tails,$F:$ at least one tail. (in $/7$)

If $A$ and $B$ are two events such that $P(\bar{A})=0.3, P(B)=0.4$ and $P(A \cap \bar{B})=0.5$, then $P(B \mid A \cup \bar{B})=$

Let $A$ and $B$ be two non-null events such that $A \subset B$. Then,which of the following statements is always correct?

Suppose that Box-$I$ contains $8$ red,$3$ blue and $5$ green balls,Box-$II$ contains $24$ red,$9$ blue and $15$ green balls,Box-$III$ contains $1$ blue,$12$ green and $3$ yellow balls,and Box-$IV$ contains $10$ green,$16$ orange and $6$ white balls. $A$ ball is chosen randomly from Box-$I$; call this ball $b$. If $b$ is red,then a ball is chosen randomly from Box-$II$; if $b$ is blue,then a ball is chosen randomly from Box-$III$; and if $b$ is green,then a ball is chosen randomly from Box-$IV$. The conditional probability of the event 'one of the chosen balls is white' given that the event 'at least one of the chosen balls is green' has happened,is equal to:

Let $A$ and $B$ be two independent events such that $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{6}$. Then,which of the following is $TRUE$?