Question

A game of chance consist of spinning an arrow, which comes to rest pointing at one of the numbers $1,2,3,4,5,6,7,8$ and these are equally likely outcomes, Find the probability that the arrows will point at any factor of $8$.

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Solution

Let's find the probability that the arrows will point at any factor of $8$.Number of events =$1,2,3,4,5,6,7,8$Total numbers: $n\left(S\right)=8\phantom{\rule{0ex}{0ex}}Factorof8=1,2,4and8\phantom{\rule{0ex}{0ex}}Numberoffactorn\left(E\right)=4\phantom{\rule{0ex}{0ex}}Therefore,probability=\frac{n\left(E\right)}{n\left(S\right)}=\frac{4}{8}\phantom{\rule{0ex}{0ex}}Probability=\frac{1}{2}$Hence, the required answer is $\frac{1}{2}$.

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