There are $10$ pairs of shoes in a cupboard from which $4$ shoes are picked at random. The probability that there is at least one pair, is

A card is drawn at random from a well shuffled pack of $52$ cards. The probability of getting a two of heart or diamond 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 persons each make a single throw with a die. The probability they get equal value is ${p_1}$. Four persons each make a single throw and probability of three being equal is ${p_2}$, then

Two dice are thrown. The probability that the sum of numbers appearing is more than $10$, is

A dice is thrown twice. The probability of getting $4, 5$ or $6$ in the first throw and $1, 2, 3$ or $4$ in the second throw is