Probability Tes...

If $$E_{1}$$ and $$E_{2}$$ are mutually exclusice events, then 

If $$P(A) = 0.45, P(B) = 0.20, P (A \cap B) = 0.15$$, then $$P(\bar{A} \cap \bar{B})$$ = 

Let $$P(E)$$ denotes probability of an event $$E$$, if $$P(B)=\dfrac{3}{4},P(A \cap B \cap \bar {C})=\dfrac{1}{3}, p(\bar {A} \cap B \cap \bar {C})=\dfrac{1}{3}$$, then $$p(B \cap C)=$$

If P (E) =0.83 then P $$\left( \overline { E } \right) =----$$

A college offers 6 courses in the morning and 4 in the evening. The possible numbers of choices with the student if he wants to study one course in the morning and one in the evening is

If A and B are even such that $$P(A \cup B)=\frac{3}{4}, P(A\cap B)=\frac{1}{4},P(\bar{A})=\frac{2}{3}, then P(\bar{A} \cap B)$$  is:

If the probability of X to fail in the examination is 0.3 and that for Y is 0.2, then the probability that either X or Y fails in the examination is :

If $$P\left( A \right) = 0.8,P\left( B \right) = 0.5,$$ then $$P\left( {A \cap B} \right)$$ lies in interval. 

Let A, B, C be three events such that :
$$P\left(A\right) = 0.3, P\left(B\right) = 0.4, P\left(C\right) = 0.5,P\left(A\cap { B }^{ ' }\right)=0.2,P\left(B\cap C\right)=0.3,P\left({ A }^{ ' }\cap { B }^{ ' }\cap { C }^{ ' }\right)=0.3$$ and $$P\left({ A\cap B }|{ C }^{ ' }\right)=0.1$$. Find the value of $$P\left({ B }^{ ' }|{ C }^{ ' }\right)$$

If  $$A$$  and  $$B$$  are two events such that  $$P ( A ) = 1 / 2$$  and  $$P ( B ) = 2 / 3 ,$$  then  $$P \left( A ^ { \prime } \cap B \right)$$  may be