Two dice are thrown simultaneously. What is the probability of obtaining a sum of the numbers less than $11$?

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three persons apply for the same house is

Two dice are thrown and the sum of the numbers appeared on the dice is noted. If $A$ is the event of getting a prime number as their sum and $B$ is the event of getting a number greater than $8$ as their sum,then $P(A \cap \overline{B})=$

If $A$ and $B$ are any two events,then the probability that exactly one of them occurs is

The probabilities of an anti-aircraft gun shooting down an enemy plane in the first,second,and third shots are $0.6, 0.7$,and $0.1$ respectively. What is the probability that the gun shoots down the plane?

For two events $A$ and $B$,if $P(A \cup B) = \frac{5}{6}$,$P(A) = \frac{1}{6}$,and $P(B) = \frac{2}{3}$,then $A$ and $B$ are: