Probability Tes...

If A and B are two events such that $$ P\left ( A \right )=\dfrac{3}{8},  P\left ( B \right )= \dfrac{5}{8}$$  and  $$P\left ( A\cup B \right )=\dfrac{3}{4}$$,  then $$P\left ( A\cap \bar{B} \right )=$$

If A and B are two mutually exclusive events such that $$P\left ( A \right )= 0.55$$  and  $$P\left ( B \right ) = 0.35$$  then  $$P\left ( \bar{A}\cup \bar{B}\right )= $$

If A and B are two events such that $$P\left ( A \right )= \dfrac{1}{4}; P\left ( A\cup B \right )=\dfrac{1}{3}$$ and  $$P\left ( B \right )= P$$ , the value of P if A and B are mutually exclusive is

If A and B are two events such that $$P\left ( A \right )=\dfrac{1}{4}; P\left ( A\cup B \right )=\dfrac{1}{3}$$ and $$ P\left ( B \right )=p$$, the value of $$p$$ if A and B are independent is

If $$P\left ( A\cup B \right )= 0.8,  P\left ( A\cap B \right )= 0.3$$, then $$P\left ( \bar{A} \right )+P\left ( \bar{B} \right )= $$

The probability that at least one of the events $$A$$ and $$B$$ occurs is $$0.7$$ and they occur simultaneously with probability $$0.2.$$ Then $$P\left( \overline { A }  \right) +P\left( \overline { B }  \right) =$$

If A and B are two mutually exclusive events such that $$P\left ( A \right )= \frac{1}{2}P\left ( B \right )$$ and $$A\cup B= S$$ the sample space, then $$P\left ( A \right )$$

A random variable $$X$$ has the probability distribution
$$X=x :  \ \ \ \ \ \ \ \ 1 \quad,2\quad, 3\quad, 4\quad, 5\quad, 6\quad, 7\quad, 8$$
$$P(X) :  \  \  \ 0.15, 0.23, 0.12, 0.1, 0.2, 0.08, 0.07, 0.05$$
Events $$E=$$ {X is a prime number} and
$$F= {X / X <4}$$
 $$i:p\overline{(E\cup F )}=0.23$$
$$ii:p(\bar{E}\cup \bar{F})=0.65$$
Which of$$ I, II$$ is (are) true $$?$$

Three numbers are chosen at random withoutreplacement from the set of integers $${1, 2, 3,....10}$$. The probability that the minimum of the chosen numbers is $$3$$ or the maximum of the chosen numbers is $$7$$, is equal to

A and B are mutually exclusive events, then