Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose.
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding stimulus
Model Answer
Total cards = numbers from 10 to 74 = 65 cards
(i) Probability of drawing an even number:
Even numbers from 10 to 74: 10, 12, 14, … 74 → 33 numbers
$$P(\text{even}) = \frac{33}{65}$$
(ii) Probability of drawing an odd number less than 30:
Odd numbers from 10 to 29: 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 → 10 numbers
$$P(\text{odd} < 30) = \frac{10}{65} = \frac{2}{13}$$
(iii) Probability of drawing a prime number between 50 and 74:
Prime numbers between 50 and 74: 53, 59, 61, 67, 71, 73 → 6 numbers
$$P(\text{prime between 50 and 74}) = \frac{6}{65}$$
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Explanation
- Total outcomes: Cards are numbered 10 to 74, so total = 74 − 10 + 1 = 65.
- For (i), count even numbers using AP: first = 10, last = 74, common difference = 2 → n = (74−10)/2 + 1 = 33.
- For (ii), odd numbers from 11 to 29: count = (29−11)/2 + 1 = 10. Simplify the fraction.
- For (iii), carefully list primes between 50 and 74 — 51, 55, 57, 65, 69 etc. are NOT prime. Only 53, 59, 61, 67, 71, 73 qualify. Examiners award marks for correct listing.