Question

A bag contains cards numbered from 5 to 100 such that each card bears a different number. A card is drawn at random. Find the probability that the number on the card is:

• [(i)] a perfect square
• [(ii)] a 2-digit number

Hint:

Count favourable outcomes and divide by total outcomes to find probability.

Answer 1

Given:
Cards numbered from 5 to 100, each with a different number.

Total number of cards:
\[ 100 - 5 + 1 = 96 \]

Part (i): Probability that the number on the card is a perfect square
Perfect squares between 5 and 100 are:
\[ 9 (3^2), 16 (4^2), 25 (5^2), 36 (6^2), 49 (7^2), 64 (8^2), 81 (9^2), 100 (10^2) \] Number of perfect squares = 8
Therefore,
\[ \text{Probability} = \frac{8}{96} = \frac{1}{12} \]

Part (ii): Probability that the number on the card is a 2-digit number
Two-digit numbers between 5 and 100 are from 10 to 99.
Number of two-digit numbers = \(99 - 10 + 1 = 90\)
Therefore,
\[ \text{Probability} = \frac{90}{96} = \frac{15}{16} \]

Final Answer:
(i) \(\frac{1}{12}\)
(ii) \(\frac{15}{16}\)