Let $A = \{ x \in R : | x + 1 | < 2 \}$ and $B = \{ x \in R : | x - 1 | \geq 2 \}$. Then which one of the following statements is $NOT$ true?

If $P(A^c) = 0.3$,$P(B) = 0.4$,and $P(A \cap B^c) = 0.5$,then find $P[B / (A \cup B)^c]$.

Let $n(U) = 700, n(A) = 200, n(B) = 300$ and $n(A \cap B) = 100,$ then $n(A^c \cap B^c) = $

Twenty persons arrive in a town having $3$ hotels $x, y$ and $z$. If each person randomly chooses one of these hotels,then what is the probability that at least $2$ of them go to hotel $x$,at least $1$ to hotel $y$,and at least $1$ to hotel $z$? (Each hotel has a capacity for more than $20$ guests.)

An electronic assembly consists of two subsystems $A$ and $B$. Past testing procedures data show that probabilities of failure are $P(A \text{ fails}) = 0.2$, $P(B \text{ fails alone}) = 0.15$, and $P(A \cap B \text{ fail}) = 0.15$. Then the probability that $A$ fails alone is equal to

If the probabilities of a student succeeding in the entrance tests for institutes $A$, $B$ and $C$ are $0.6$, $0.5$ and $0.4$ respectively, while the probability of succeeding in both $A$ and $B$ is $0.3$, in both $B$ and $C$ is $0.2$, in both $A$ and $C$ is $0.2$, and in all three is $0.1$, then the probability that the student succeeds in exactly one of these tests is......