A box contains 120 discs, which are numbered from 1 to 120. If one disc is drawn at random from the box, find the probability that: a) it bears a 2- digit number b) the number is a perfect square.

A box contains 120 discs, which are numbered from 1 to 120. If one disc is drawn at random from the box, find the probability that:

We are given a box containing $120$ discs numbered from $1$ to $120$. A disc is drawn at random, and we need to find the probability of the following events:

### (a) Probability of Drawing a Two-Digit Number

A two-digit number ranges from $10$ to $99$. The total count of such numbers is:

$99 - 10 + 1 = 90$

Since there are $120$ discs, the probability is:

$ \displaystyle P(\text{two-digit number}) = \frac{90}{120} = \frac{3}{4} $

### (b) Probability of Drawing a Perfect Square

Perfect squares between $1$ and $120$ are:

$1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121$

Since $121$ is out of range, the valid perfect squares are:

$1, 4, 9, 16, 25, 36, 49, 64, 81, 100$

Total count = $10$

The probability is:

$ \displaystyle P(\text{perfect square}) = \frac{10}{120} = \frac{1}{12} $

### Final Answer:
(a) $ \frac{3}{4} $
(b) $ \frac{1}{12} $

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