Probability Tes...

For any two independent events $$E_{1}$$ and $$E_{2}$$ in a space $$S, P[(E_{1} \cup E_{2})\cap (E_{1}\cap E_{2})]$$ is equal to

If $$A$$ and $$B$$ are two events, then, $$1+P\left( A\cap B \right) -P\left( B \right) -P\left( A \right) $$ is equal to

If the events $$A$$ and $$B$$ are independent and if $$P(\overline {A}) = \dfrac {2}{3}, P(\overline {B}) = \dfrac {2}{7}$$, then $$P(A\cap B)$$ is equal to

The probabilities that Mr. $$A$$ and Mr. $$B$$ will die within a year are $$\dfrac { 1 }{ 2 } $$ and $$\dfrac { 1 }{ 3 } $$ respectively, then the probability that only one of them will be alive at the end of the year, is

The probabilities of solving a problem by three students $$A,B$$ and $$C$$ are $$\cfrac { 1 }{ 2 } ,\cfrac { 3 }{ 4 } $$ and $$\cfrac { 1 }{ 4 } $$ respectively. The probability that the problem will be solved is

Out of $$50$$ tickets numbered $$00, 01, 02, ...., 49$$ one ticket is drawn randomly, the probability of the ticket having the product of its digits $$7$$ given that the sum of the digits is $$8$$, is

If $$A$$ and $$B$$ are two events such that $$P(A) = \dfrac {3}{4}$$ and $$P(B) = \dfrac {5}{8}$$, then

If $$P(A) = 65, P(B) = 80$$, then $$P(A\cap B)$$ lies in the interval

Let $$A$$ and $$B$$ be two events such that $$P (A \cup B) = P(A) + P(B)- P (A) P(B)$$. If $$0 < P(A) < 1$$ and $$0 < P (B) < 1$$, then $$P(A \cup B)'$$ is equal to

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 $$Y$$ fail in the examination is