Probability Tes...

If A and B are two events in a sample space S such that $$P\left ( A \right )\neq 0$$  and  $$P\left ( B \right )\neq 0$$,  then  $$P\left ( A\cap B \right )$$

If A and B are two events such that  $$P\left ( A \right )> 0$$  and  $$P\left ( B \right )\neq 1$$,  then  $$P\left ( \bar{A}/\bar{B} \right )= $$

If A and B are two events in a sample space S such that $$P\left ( A \right )\neq 0$$,  then  $$P\left ( \frac{B}{A} \right )= $$

If $$P\left ( {B \ |A} \right )< P\left ( B \right )$$ the relationship between $$P ( {A \ |B}  )$$ and $$P\left ( A \right )$$ is

The probability that a bulb produced by a factory will fuse after $$100$$ days of use is $$0.05$$. The probability that out of $$5$$ such bulbs not more than one will fuse after $$100$$ days is

If A and B are mutually exclusive events with $$P\left ( B \right )\neq 1$$, then  $$P\left ( A\mid \bar{B} \right )= $$

If  $$P\left ( \dfrac{A}{C} \right )> P\left ( \dfrac{B}{C} \right )$$  and  $$P\left ( \dfrac{A}{\bar{C}} \right )> P\left ( \dfrac{B}{\bar{C}} \right )$$  then the relationship between $$P(A)$$ and $$P(B)$$ is

A couple has $$2$$ children. The probability that both are boys, if it is known that at least one of the children is a boy is

If $$\overline { E } $$ and $$\overline { F } $$ are the complementary events of events $$E$$ and $$F$$ respectively and if $$0<P(F)<1$$, then

Each of the urns contains $$4$$ white and $$6$$ blackballs. The (n + 1)th urn contains $$5$$ white and $$5$$black balls. One of the (n+1) urns is chosen atrandom and two balls are drawn from it withoutreplacement and both the balls turn out to beblack. Then the probability that the (n+1)th urn was chosen to draw the balls is $$1/16$$, the value of n is