Probability Tes...

If the probability of $$A$$ to fail in an examination is $$\displaystyle \frac {1}{5}$$ and that of $$B$$ is $$\displaystyle \frac {3}{10}$$ then the probability that either $$A$$ or $$B$$ fails is

Three numbers are chosen at random without replacement from $$1, 2, 3, ... , 10$$. The probability that the minimum of the chosen numbers is $$4$$ or their maximum is $$8$$, is

Let $$A$$ and $$B$$ be two independent events such that $$\displaystyle P(A) = \frac {1}{5}, P(A \cup B) = \frac {7}{10}$$. Then $$\displaystyle P (\overline B)$$ is equal to

Three numbers are chosen at random without replacement from $${1,2,...10}$$. The probability that the minimum of the chosen numbers is $$3$$, or their maximum is $$7$$, is

For two events $$A$$ and $$B$$ if $$\displaystyle P\left( A \right) =P\left( \frac { A }{ B }  \right) =\frac { 1 }{ 4 } $$ and $$\displaystyle P\left( \frac { B }{ A }  \right) =\frac { 1 }{ 2 } $$, then

If two events $$A$$ and $$B$$ are such that $$P\left( A' \right) =0.3,P\left( B \right) =0.4$$ and $$P\left( AB' \right) =0.5$$, then $$\displaystyle P\left( \frac { B }{ \left( A\cup B' \right)  }  \right) =$$

If $$P\left( { E }_{ 1 } \right) =0.2,P\left( { E }_{ 2 } \right) =0.4$$ and $$P\left( { E }_{ 3 } \right) =0.6$$ and $${ E }_{ 1 },{ E }_{ 2 }$$ and $${ E }_{ 3 }$$ are independent events, then the probability that at least one of these events $${ E }_{ 1 },{ E }_{ 2 }$$ and $${ E }_{ 3 }$$ occurs is

Four cards are drawn at a time from a pack of $$52$$ playing cards. Find the probability of getting all the $$4$$ cards of the same suit.

The probability that the least one of the events $$A$$ and $$B$$ occur is $$0.6$$, if $$A$$ and $$B$$ occur simultaneously with probability $$0.2$$, then $$P(\bar { A })+ P(\bar { B } )$$, where $$\bar A$$ and $$\bar B$$ are complements of $$A$$ and $$B$$ respectively is equal to

$$A$$ and $$B$$ are two independent events. The probability that both $$A$$ and $$B$$ occur is $$1/6$$ and the probability that at least one of them occurs is $$\cfrac{2}{3}$$. The probability of the occurrence of $$A=$$............ if $$P(A)=2P(B)$$.