If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A | B).$

If $C$ and $D$ are two events such that $C \subset D$ and $P(D) \neq 0$,then which of the following is true?

Two cards are drawn from a pack of $52$ playing cards one after the other. If $p_1$ is the probability of getting a queen in the first draw and a diamond card in the second draw when the first card drawn is replaced, and $p_2$ is the probability of the same event when the first card drawn is not replaced, then $\frac{p_1}{p_2} = $

Four fair dice $D_1, D_2, D_3$ and $D_4$,each having six faces numbered $1, 2, 3, 4, 5$ and $6$,are rolled simultaneously. The probability that $D_4$ shows a number appearing on at least one of $D_1, D_2$ and $D_3$ is

If $E_1$ and $E_2$ are two events of a sample space such that $P(E_1) = \frac{1}{4}$,$P(E_2 \mid E_1) = \frac{1}{2}$,and $P(E_1 \mid E_2) = \frac{1}{4}$,then $P(\bar{E}_1 \mid E_2) = $

If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A \cap B).$