Q.A drawing pin was tossed 500 times, and it landed 'point up' 316 times. Using the relative-frequency (empirical) approach, estimate the probability that the pin lands point up on the next toss.

For any event $A$, $0\le P(A)\le1$.

By the axiomatic definition of probability, the probability of any event $A$ of the sample space satisfies $0\le P(A)\le1$. It cannot be negative and cannot exceed $1$. Option (b) is written with contradictory inequality signs and is invalid.

A non-leap February has $28$ days $= 4$ full weeks, so every day of the week appears exactly $4$ times; getting $5$ Mondays is impossible, probability $= 0$ — option (a).

GSEB Class-12 Statistics, Probability:

In a non-leap year, February has $28$ days.

$28 = 4 \times 7$

Since $28$ is an exact multiple of $7$, the month contains exactly $4$ complete weeks and no extra days. Therefore each weekday, including Monday, occurs exactly 4 times.

A 5th Monday cannot occur, so the event is impossible:

$P(5 \text{ Mondays}) = 0$

The classical definition of probability is also known as the mathematical (a priori) definition.

Reasoning. The classical approach defines $P(A) = \dfrac{\text{favourable outcomes}}{\text{total equally likely outcomes}}$ purely by reasoning/counting, before any experiment. Hence it is called the mathematical or a priori definition, distinct from the statistical (relative-frequency) and axiomatic definitions.