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

$A$ 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 two events $A$ and $B$ are such that $P(A^c) = 0.3$,$P(B) = 0.4$ and $P(A \cap B^c) = 0.5$,then $P(B | A \cup B^c)$ is equal to

If $P(A) = \frac{1}{2}$ and $P(B) = 0$,then $P(A | B)$ is

$A$ die is thrown. If $E$ is the event 'the number appearing is a multiple of $3$' and $F$ is the event 'the number appearing is even',then find whether $E$ and $F$ are independent?

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is