Probability Tes...

Roll a fair die twice. Let $$A$$ be the even that the sum of the two rolls equals six, and let $$B$$ be the even that the same  number comes up twice. What is $$P(A/B)$$?

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :

If two events A and B are such that  $$P ( \overline { A } ) = \dfrac { 3 } { 10 } , P ( B ) = \dfrac { 2 } { 5 }$$ and $$P ( A \cap \overline { B } ) = \dfrac { 1 } { 2 }$$ ,then $$P \left( \dfrac { B } { A \cup \overline { B } } \right)$$ is

A natural number is chosen at random from amongest the first $$500$$. The probability that the number chosen is divisible by $$3$$ or $$5$$ is ? .

If $$C\ and D$$ are two events such that $$C\subset D$$  and  $$P\left( D \right) \neq 0$$, then the correct statement among the following is: 

A letter is known to have come either from $$'KRISHNAGIRI'$$ or $$'DHARMPURI'$$. On the post mark only the two consecutive letters $$'RI$$ are visible. Then, the chance that it come from $$'KRISHNAGIRI'$$ is

A random variable $$X$$ has the probability distribution:

$$X$$:	1	2	3	4	5	6	7	8
$$p(X)$$:	0.2	0.2	0.1	0.1	0.2	0.1	0.1	0.1

For the events $$E=\left\{ X\quad is\quad a\quad prime\quad number \right\} $$ and $$F=\left\{ X<4 \right\} $$, the $$P(E\cup F)$$ is

If $$A$$ and $$B$$ are two events such that $$P(A)=0.3,\ P(B)=0.6$$ and $$P(B/A)=0.5$$ then $$P(A/B)$$=

The total number of ways of selecting six coins out of 20 one-rupee coins, 10 fifty-paise coins, and 7 twenty- five paise coins is:

A natural number $$x$$ is chosen at random from the first $$120$$ natural numbers and it is observed to be divisible by $$8 ,$$ then the probability that it is not divisible by $$6$$ is