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

If $A$ and $B$ are any two events such that $P(A) = \frac{2}{5}$ and $P(A \cap B) = \frac{3}{20}$,then the conditional probability $P(A | A' \cup B')$,where $A'$ denotes the complement of $A$,is equal to:

$A$ candidate takes three tests in succession and the probability of passing the first test is $p$. The probability of passing each succeeding test is $p$ if he passes the preceding one, and $\frac{p}{2}$ if he fails the preceding one. The candidate is selected if he passes at least two tests. The probability that the candidate is selected is:

Let $A$ and $B$ be two independent events such that $P(A) + P(B) = \frac{3}{4}$ and $P(\overline{A} | B) = \frac{2}{5}$. Then,$P(A \cap B)$ is -

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?

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