If $A$ and $B$ are arbitrary events, then
$P(A \cap B) \ge P(A) + P(B)$
$P(A \cup B) \le P(A) + P(B)$
$P(A \cap B) = P(A) + P(B)$
None of these
$A, B, C$ are any three events. If $P (S)$ denotes the probability of $S$ happening then $P\,(A \cap (B \cup C)) = $
Let $A$ and $B$ be two events such that $P\,(A) = 0.3$ and $P\,(A \cup B) = 0.8$. If $A$ and $B$ are independent events, then $P(B) = $
If $E$ and $F$ are events such that $P(E)=\frac{1}{4}$, $P(F)=\frac{1}{2}$ and $P(E$ and $F )=\frac{1}{8},$ find $:$ $P($ not $E$ and not $F)$.
In a class of $60$ students, $30$ opted for $NCC$ , $32$ opted for $NSS$ and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random, find the probability that The student opted for $NCC$ or $NSS$.
One bag contains $5$ white and $4$ black balls. Another bag contains $7$ white and $9$ black balls. A ball is transferred from the first bag to the second and then a ball is drawn from second. The probability that the ball is white, is