The probabilities of a problem being solved by two students are $\frac{1}{2}$ and $\frac{1}{3}$. Then the probability of the problem being solved is

From a well-shuffled pack of cards,one card is drawn at random. The probability that the card drawn is an ace is

$A$ number is chosen at random from the first ten natural numbers. The probability that the number is odd and a perfect square is

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements:
$(S1) : \text{If } P(A) = 0, \text{ then } A = \phi$
$(S2) : \text{If } P(A) = 1, \text{ then } A = \Omega$
Then:

The probability that a number selected at random from the set of numbers $(1, 2, 3, \ldots, 100)$ is a cube,is

Three students $A, B,$ and $C$ are given a mathematics problem. The probabilities of them solving the problem are $1/2, 1/3,$ and $1/4$ respectively. What is the probability that the problem is solved?