A book

A book contains 524 pages. If it is known that a person will select any one page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253.

Correct result:

p =  0.7692 %

Solution:

$$\begin{gathered} C_1(260)=\left({\displaystyle \genfrac{}{}{0px}{}{260}{1}}\right)={\displaystyle \frac{260!}{1!(260-1)!}}={\displaystyle \frac{260}{1}}=260 \\ {C}_1(2)=\left({\displaystyle \genfrac{}{}{0px}{}{2}{1}}\right)={\displaystyle \frac{2!}{1!(2-1)!}}={\displaystyle \frac{2}{1}}=2 \\ p=100\cdot {\displaystyle \frac{\left(\genfrac{}{}{0px}{}{2}{1}\right)}{\left(\genfrac{}{}{0px}{}{384-125+1}{1}\right)}}=100\cdot {\displaystyle \frac{2}{\left(\genfrac{}{}{0px}{}{384-125+1}{1}\right)}}={\displaystyle \frac{10}{13}}=0.7692\mathrm{\%} \end{gathered}$$

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