If a number is chosen at random from the set $\{1, 2, 3, \ldots, 100\}$,then the probability that the chosen number is a perfect cube is

If $\frac{1+3P}{3}$ and $\frac{1-2P}{2}$ are probabilities of two mutually exclusive events,then $P$ lies in the interval.

If a die is thrown $2$ times,what is the probability of getting $4$ at least once?

If two balanced dice are tossed once,the probability of the event that the sum of the integers appearing on the upper faces of the two dice is $9$ is:

Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. Then the probability that $a^2 - b^2$ is divisible by $3$ is (in $/87$)

The probability that a man and his wife will be alive after $20 \text{ years}$ are $\frac{1}{4}$ and $\frac{1}{3}$ respectively. The probability that neither the man nor his wife will be alive after $20 \text{ years}$ is