When a die is thrown twice,what is the probability that the sum of the numbers is $6$,given that at least one of the numbers is $4$?

$A$ college student has to appear for two examinations $A$ and $B$. The probabilities that the student passes in $A$ and $B$ are $\frac{2}{3}$ and $\frac{3}{4}$ respectively. If it is known that the student passes at least one among the two examinations,then the probability that the student will pass both the examinations is

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

Compute $P(A | B),$ if $P(B)=0.5$ and $P(A \cap B)=0.32$.

$A$ 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:

Three dice are thrown. Given that the sum of the numbers on them is $8$,what is the probability that at least one of them shows a $4$?