If the probability of a horse $A$ winning a race is $1/4$ and the probability of a horse $B$ winning the same race is $1/5$, then the probability that either of them will win the race is

Probability of solving specific problem independently by $A$ and $B$ are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that  the problem is solved.

Let $A$ and $B $ be two events such that  $P\left( {\overline {A \cup B} } \right) = \frac{1}{6}\;,P\left( {A \cap B} \right) = \frac{1}{4}$ and $P\left( {\bar A} \right) = \frac{1}{4}$ where $\bar A$ stands for the complement of the event $A$. Then the events $A$ and$B$ are

Three ships $A, B$ and $C$ sail from England to India. If the ratio of their arriving safely are $2 : 5, 3 : 7$ and $6 : 11$ respectively then the probability of all the ships for arriving safely is

If $P(A) = P(B) = x$ and $P(A \cap B) = P(A' \cap B') = \frac{1}{3}$, then $x = $