An integer is chosen at random from first 200 positive integers. … - Vidyadip

Question

An integer is chosen at random from first 200 positive integers. Find the probability that the integer is divisible by 6 or 8.

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Answer

Let A be the event of choosing a positive integer divisible by 6 $\therefore\text{A}=\{6,\ 12,\ ....,\ 198\}$ $\Rightarrow\text{n}(\text{A})=33$ $\therefore\text{p}(\text{A})=\frac{33}{200}$ Let B be the event of choosing a positive integer divisible by 8 $\therefore\text{B}=\{8,\ 16,\ ....,\ 200\}$ $\Rightarrow\text{n}(\text{B})=25$ $\therefore\text{p}(\text{B})=\frac{25}{200}$ Also, $\text{A}\cap\text{B}=\{24,\ 28,\ ...,\ 192\}$ $\Rightarrow\text{n}(\text{A}\cap\text{B})=8$ $\therefore\text{p}(\text{A}\cap\text{B})=\frac{8}{200}$ $\therefore\text{p}(\text{A}\cup\text{B})=\frac{1}{4}$

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