A pair of a dice thrown, if $5$ appears on at least one of the dice, then the probability that the sum is $10$ or greater is

In a throw of a dice the probability of getting one in even number of throw is

Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happen is $\frac{1}{12}$ and the probability that neither $E$ nor $F$ happens is  $\frac{1}{2}$ , then a value of  $\frac{{P(E)}}{{P\left( F \right)}}$ is

If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is

Two numbers are selected randomly from the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ without replacement one by one. The probability that minimum of the two numbers is divisible by $3$ or maximum of the two numbers is divisible by $4$ , is 

If three students $A, B, C$ independently solve a problem with probabilitities $\frac{1}{3},\frac{1}{4}$ and $\frac{1}{5}$ respectively, then the probability that the problem will be solved is