Probability Tes...

Suppose A and B are two events. Event B has occured and it is known that $$P(B) <1$$. What is $$P(A|B^c)$$ equal to?

Probability of impossible event is

A researcher conducted a survey to determine whether people in a certain town prefer watching sports on television to attending the sporting event. The researcher asked 117 people who visited a local restaurant on a Saturday, and 7 people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about the sports-watching preferences of all people in the town?

For two independent events $$A$$ and $$B$$, what is $$P(A + B)$$, given $$P(A) = \dfrac{3}{5}$$ and $$P(B) = \dfrac{2}{3}$$?

If $$\dfrac{1+3p}{3},\dfrac{1-2p}{2} $$ are probabilities of two mutually exclusive event, then $$p$$ lies in the interval 

There are two bags, one of which contains $$3$$ black and $$4$$ white balls,$$II$$ bag contain $$4$$ black and $$3$$ white balls.A die is cast, if the number $$3$$ or less than $$3$$ turns up, a ball is drawn from $$1$$ bag and if the face greater than $$3$$ turns up, a ball is drawn from $$II$$ bag. It is found that ball drawn is black. Find the probability that it is from bag I.

The probability that an event does not happens in one trial is 0.8.The probability that the event happens atmost once in three trails is 

A box contains $$2$$ silver coins and 4 gold coins and the second box contains $$4$$ silver coins and $$3$$ gold coins. If a coin is selected from one of the box, what is the probability that it is a silver coin. 

Two events $$A$$ and $$B$$ are such that
$$P(A)=\cfrac { 1 }{ 4 } ,P(A|B)=\cfrac { 1 }{ 4 } $$ and $$P(B|A)=\cfrac { 1 }{ 2 } $$
Consider the following statements:
(I) $$P(\overline { A } |\overline { B } )=\cfrac { 3 }{ 4 } $$
(II) $$A$$ and $$B$$ are mutually exclusive
(III) $$P(A|B)+P(A|\overline { B } )=1$$
Then

$$A, B$$ and $$C$$ are three mutually exclusive and exhaustive events such that $$P(A) = 2P(B) = 3P(C)$$.
What is $$P(B)$$?