If $4\,P(A) = 6\,P(B) = 10\,P(A \cap B) = 1$,then $P\left( \frac{B}{A} \right) = \dots$

$A$ cubical die with faces marked $1, 2, 3, ..., 6$ is tossed such that the probability of throwing the number $t$ is proportional to $t^2$. The probability that the number $5$ has appeared,given that the number turned up is not even,is:

If $A$ and $B$ are any two events such that $P(A)+P(B)-P(A \cap B)=P(A)$,then

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$,given that $5$ appears on the first die?

$A$ bag contains $3$ red and $7$ black balls. Two balls are taken out at random,without replacement. If the first ball taken out is red,what is the probability that the second ball taken out is also red?

$A$ die is thrown twice and the sum of the numbers appearing is observed to be $6$. What is the conditional probability that the number $4$ has appeared at least once?