Question:
When a single number is drawn at random from the first 20 positive natural numbers, the probability that it is a multiple of 4 but NOT a multiple of 6 is equal to:
When a single number is drawn at random from the first 20 positive natural numbers, the probability that it is a multiple of 4 but NOT a multiple of 6 is equal to:
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Remove numbers divisible by both 4 and 6 (i.e., multiples of 12).
Updated On: Jun 12, 2026
- $\frac{1}{5}$
- $\frac{1}{4}$
- $\frac{2}{5}$
- $\frac{3}{4}$
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The Correct Option is A
Solution and Explanation
Step 1: Find the sample space. The first 20 natural numbers are: $$ 1,2,3,\ldots,20 $$ Hence, $$ n(S)=20 $$
Step 2: Find favourable outcomes. Multiples of $4$ up to $20$ are: $$ 4,8,12,16,20 $$ Among these, $12$ is also a multiple of $6$. Therefore favourable numbers are: $$ 4,8,16,20 $$ Hence, $$ n(E)=4 $$
Step 3: Compute probability. $$ P(E)=\frac{4}{20}=\frac{1}{5} $$ \[ \boxed{\frac{1}{5}} \]
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