Cards numbered 2 to 101 are in a box (100 cards). Probability that the card has (i) an even number (ii) a square number?
(i) \(\dfrac{1}{2}\), (ii) \(\dfrac{9}{100}\)
Step 1: Total number of cards = 100 (since numbers are from 2 to 101).
Part (i): Probability of an even number
• Even numbers are those divisible by 2 (like 2, 4, 6, ...).
• From 2 to 101, half of the numbers are even and half are odd.
• Total even numbers = 50.
• Probability = (Number of favourable cases) ÷ (Total cases)
• Probability = \(\dfrac{50}{100} = \dfrac{1}{2}\).
Part (ii): Probability of a square number
• A square number is of the form \(n^2\), where \(n\) is a whole number.
• The first square ≥ 2 is \(2^2 = 4\).
• The largest square ≤ 101 is \(10^2 = 100\).
• So the square numbers between 2 and 101 are: 4, 9, 16, 25, 36, 49, 64, 81, 100.
• Total = 9 square numbers.
• Probability = \(\dfrac{9}{100}\).
Final Answer:
(i) \(\dfrac{1}{2}\), (ii) \(\dfrac{9}{100}\).