If out of $20$ consecutive whole numbers two are chosen at random,then the probability that their sum is odd,is

From a pack of $52$ cards,$4$ cards are drawn. What is the probability that it has two digit-cards and one honours card of black suit and one honours card of red suit?

Two dice are thrown. Find the probability of getting an even number as the sum.

There are $3$ bags which are known to contain $2$ white and $3$ black balls; $4$ white and $1$ black balls and $3$ white and $7$ black balls respectively. $A$ ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black balls is

$A$ mapping is selected at random from the set of all the mappings of the set $A = \{1, 2, ..., n\}$ into itself. The probability that the mapping selected is an injection is

In a college,$25\%$ of the boys and $10\%$ of the girls offer Mathematics. The girls constitute $60\%$ of the total number of students. If a student is selected at random and is found to be studying Mathematics,the probability that the student is a girl,is