Probability Tes...

Suppose $$A$$ and $$B$$ are two events with $$P(A)=0.5$$ and $$P(A \cup B) =0.8$$. Let $$P(B)=p$$ if $$A$$ and $$B$$ are mutually exclusive and $$P(B)=q$$ if $$A$$ and $$B$$ are independent events, then the value of $$q/p$$ is

Let  A and B be two events. Suppose $$P(A)=0.4, P(B)=p$$, and $$P(A \cup B) = 0.7 $$. The value of $$p$$ for which A and B are independent is

If $$P (A \cup B) = \dfrac{2}{3} ,  P (A \cap B) = \dfrac{1}{6} $$  and $$ P(A) = \dfrac{1}{3}$$ then -

If odds against solving a question by three students are 2:1, 5:2 and 5:3 , respectively, then probability that the question is solved only by one student is

If $$P( A \cup B )=\displaystyle\frac{3}{4}$$ and $$P( \bar A)= \displaystyle\frac{2}{3}$$, then find the value of $$P( \bar A \cap B )$$.

A bag contains $$3$$ white, $$3$$ black, and $$2$$ red balls. One by one three balls are drawn without replacing them, then find the probability that the third ball is red.

Let $$A$$ and $$B$$ be two events such that $$\displaystyle P(\overline{A\cup B})=\frac{1}{6},P(A\cap B)=\frac{1}{4}$$ and $$P(\bar{A})=\dfrac{1}{4}$$ where $$\bar{A}=$$ complementary of event $$A$$. Then $$A$$ and $$B$$ are

For any two independent events $${ E }_{ 1 }$$ and $${ E }_{ 2 },P\left\{ \left( { E }_{ 1 }\cup { E }_{ 2 } \right) \cap \left( \overline { { E }_{ 1 } }  \right) \cap \left( \overline { { E }_{ 2 } }  \right)  \right\} $$ is 

$$A$$ and $$B$$ are two events where $$P(A) = 0.25$$ and $$P(B) = 0.5$$. The probability of both happening together is $$0.14$$. The probability of both $$A$$ and $$B$$ not happening is

If $$\displaystyle P\left ( B \right )= \frac{3}{4}, P\left ( A\cap B\cap \bar{C} \right )=\frac{1}{3}$$ and $$\displaystyle P\left ( \bar{A}\cap B\cap \bar{C} \right )=\frac{1}{3}$$ then $$\displaystyle P\left ( B\cap C \right )$$ is