A die is loaded in such a way that each odd number is twice as likely to occur as each even number. If $E$ is the event that a number greater than or equal to $4$ occurs on a single toss of the die then $P(E)$ is equal to
$\frac{4}{9}$
$\frac{2}{3}$
$\frac{1}{3}$
$\frac{1}{2}$
If $P\,(A) = \frac{1}{4},\,\,P\,(B) = \frac{5}{8}$ and $P\,(A \cup B) = \frac{3}{4},$ then $P\,(A \cap B) = $
True statement $A$ and true statement $B$ are two independent events of an experiment.Let $P\left( A \right) = 0.3$ , $P\left( {A \vee B} \right) = 0.8$ then $P\left( {A \to B} \right)$ is (where $P(X)$ denotes probability that statement $X$ is true statement)
An integer is chosen at random from the integers $\{1,2,3, \ldots \ldots . .50\}$. The probability that the chosen integer is a multiple of atleast one of $4,6$ and $7$ is
One card is drawn randomly from a pack of $52$ cards, then the probability that it is a king or spade is
If $P(A) = 0.25,\,\,P(B) = 0.50$ and $P(A \cap B) = 0.14,$ then $P(A \cap \bar B)$ is equal to