Probability Tes...

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

If P(A) = P(B), then

$$A$$ and $$B$$ are two events such that $$P(A\cup B) = \dfrac {3}{4}, P(A\cap B) = \dfrac {1}{4}, P(\overline {A}) = \dfrac {2}{3}$$; then $$P(\overline {A} \cap B)$$ is

If $$A$$ and $$B$$ are mutually exclusive events, then

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 $$P(B)$$?

If for two events $$A$$ and $$B, P(A\cap B)\ne P(A) \times P(B)$$, then the two events $$A$$ and $$B$$ are

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 $$A, B$$ and $$C$$ are mutually exclusive and exhaustive events, then $$P(A) + P(B) + P(C)$$ equals to - 

Let $$A$$ and $$B$$ be subsets of $$X$$ and $$C=\left( A\cap B' \right) \cup \left( A'\cap B \right) $$ where $$A'$$ and $$B'$$ are complements of $$A$$ and $$B$$ respectively in $$X$$. What is $$C$$ equal to?