A card is drawn at random from a box containing 12 cards numbered 1,2,3,4,5,….,12. Find the probability of drawing (i) ‘8’, (ii) an even number, (iii) a perfect square, (iv) a negative number and (v) a number less than 13.
Answer: see the solution
Explanation
Total number of cards: 12
(i) Probability of drawing '8'
- Favorable outcomes: 1 (card number 8)
- Probability: 1/12
(ii) Probability of drawing an even number
- Favorable outcomes: 6 (2, 4, 6, 8, 10, 12)
- Probability: 6/12 = 1/2
(iii) Probability of drawing a perfect square
- Favorable outcomes: 4 (1, 4, 9)
- Probability: 4/12 = 1/3
(iv) Probability of drawing a negative number
- Favorable outcomes: 0 (no negative numbers)
- Probability: 0/12 = 0
(v) Probability of drawing a number less than 13
- Favorable outcomes: 12 (all cards are less than 13)
- Probability: 12/12 = 1
In summary:
- Probability of drawing '8': 1/12
- Probability of drawing an even number: 1/2
- Probability of drawing a perfect square: 1/3
- Probability of drawing a negative number: 0
- Probability of drawing a number less than 13: 1
