A box contains $20$ cards numbered from $1$ to $20$. A card is drawn at random. Find the probability that the number on the card is:
(i) An even number
(ii) Divisible by $2$ or $3$
(iii) A prime number
Step-by-Step Solution
Key Concept: Total $= 20$.<br>(i) Even: $2, 4, \dots, 20 = 10 \Rightarrow P = 10/20 = 1/2$.<br>(ii) Divisible by 2 or 3: $2,3,4,6,8,9,10,12,14,15,16,18,20 = 13 \Rightarrow P = 13/20$.<br>(iii) Prime: $2, 3, 5, 7, 11, 13, 17, 19 = 8 \Rightarrow P = 8/20 = 2/5$.
(i) $P(\text{Even}) = 10/20 = 1/2$. [1.0 Mark]
(ii) $P(\text{Divisible by 2 or 3}) = 13/20$. [1.0 Mark]
(iii) $P(\text{Prime}) = 8/20 = 2/5$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Part (i) $P = 1/2$: 1.0 Mark
Part (ii) $P = 13/20$: 1.0 Mark
Part (iii) $P = 2/5$: 1.0 Mark
Correct Answer: