If $A$ and $B$ are two independent events,then $A$ and $\bar{B}$ are

An electronic assembly consists of two subsystems,$A$ and $B$. From previous testing procedures,the following probabilities are known:
$P(A \text{ fails}) = 0.2$
$P(B \text{ fails alone}) = 0.15$
$P(A \text{ and } B \text{ fail}) = 0.15$
Evaluate the probability $P(A \text{ fails } | \text{ } B \text{ has failed})$.

For any two events $A$ and $B$,if $P(A) + P(B) - P(A \cap B) = P(A)$,then . . . . . . .

Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$, then the probability of non-occurrence of at least one of the events $E$ and $F$ is

For two events $A$ and $B$,if $P(A) = P\left( \frac{A}{B} \right) = \frac{1}{4}$ and $P\left( \frac{B}{A} \right) = \frac{1}{2},$ then:

Bag $P$ contains $3$ white, $2$ red, $5$ blue balls and bag $Q$ contains $2$ white, $3$ red, $5$ blue balls. $A$ ball is chosen at random from $P$ and is placed in $Q$. If a ball is chosen from bag $Q$ at random, then the probability that it is a red ball is