Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability4 Marks
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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