Probability Tes...

STATEMENT - 1 : Dependent events are those in which the outcome of one does not affect and is not affected by the other.
STATEMENT - 2 : Dependent events are those in which the outcome of one affects and is affected by the other.

If A and B are independent events,then  $$P\left ( \dfrac{B}{A} \right )= $$

If $$A$$ and $$B$$ are events such that $$P\left( A|B \right) =P\left( B|A \right) $$, then

A coin is tossed three times, where
(i) $$E$$ : head on third toss,  $$F$$ : heads on first two tosses
(ii) $$E$$ : at least tow heads,  $$F$$ : at most two heads
(iii) $$E$$ : at most two tails,  $$F$$ : at least one tail
Determine $$ P\left( E|F \right) $$ 

If $$P\left( A \right) = \displaystyle\frac { 1 }{ 2 } $$,  $$P\left( B \right) =0$$, then $$P\left( A|B \right) $$ is

Probability that $$A$$ speaks truth is $$\displaystyle\frac { 4 }{ 5 } $$. A coin is tossed. A reports that a head appears. The probability that actually there was head is

Two events $$A$$ and $$B$$ will be independent, if

If $$P\left( A \right) = \displaystyle\frac { 6 }{ 11 },   P\left( B \right) = \displaystyle\frac { 5 }{ 11 }$$ and $$ P\left( A \cup B \right) = \displaystyle\frac { 7 }{ 11 }$$, find 
(i) $$ P\left( A \cap B \right)$$
(ii) $$ P\left( A | B \right)$$
(iii) $$ P\left( B | A \right) $$

10% of tools produced by a certain manufacturing process turn out to be defective. Assuming binomial distribution, the probability of 2 defective in simple of 10 tools chosen at random, is

Difference between sample space and subset of sample space is considered as