Let $A$ and $B$ be two events with $P(A) = \frac{1}{7}$,$P(A|B) = \frac{2}{3}$,and $P(B) = \frac{2}{7}$. Then,the value of $P(B|A)$ is

For a biased die,the probabilities for different faces to turn up are given below:

$Face$	$1$	$2$	$3$	$4$	$5$	$6$
$Probability$	$0.1$	$0.32$	$0.21$	$0.15$	$0.05$	$0.17$

The die is tossed and you are told that either face $1$ or $2$ has turned up. Then the probability that it is face $1$ is:

Let $X$ and $Y$ be two events of a sample space such that $P(X)=\frac{1}{3}$, $P(X|Y)=\frac{1}{2}$ and $P(Y|X)=\frac{2}{5}$, then which of the following is true?

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 events,such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$,then $P(B)$ is

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes,the number of outcomes that $B$ must have so that $A$ and $B$ are independent,is