While dialing a telephone number,an old man forgets the last two digits,remembering only that they are different. If he dials the last two digits at random,what is the probability that the number is dialed correctly?

From the word $POSSESSIVE$, a letter is chosen at random. The probability of it being $S$ is:

$A$ bag contains $13$ red,$14$ green,and $15$ black balls. The probability of getting exactly $2$ black balls when pulling out $4$ balls is ${P_1}$. Now,the number of balls of each color is doubled,and $8$ balls are pulled out. The probability of getting exactly $4$ black balls is ${P_2}$. Then:

$A$ bag contains $3$ red,$7$ white,and $4$ black balls. If three balls are drawn from the bag,the probability that all of them are of the same color is:

If $\overline{E}$ and $\overline{F}$ are the complementary events of events $E$ and $F$ respectively and if $0 < P(F) < 1,$ then

Two numbers are selected at random from $1, 2, 3, \dots, 100$ and are multiplied. The probability, correct to two decimal places, that the product thus obtained is divisible by $3$ is: