In a box, there are $20$ cards, out of which $10$ are lebelled as $\mathrm{A}$ and the remaining $10$ are labelled as $B$. Cards are drawn at random, one after the other and with replacement, till a second $A-$card is obtained. The probability that the second $A-$card appears before the third $B-$card is

If the paper of $4$ students can be checked by any one of $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is

In a certain lottery $10,000$ tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket.

Out of all possible $8$ digit numbers formed using all the digits $0,0,1,1,2,3,4,4$ a number is randomly selected. Probability that the selected number is odd, is-

There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is

A bag contains $3$ white and $7$ red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red