First test

20 questions are prepared for a test. 3 questions are selected from them for the first test and then returned to the list. What is the probability that when selecting questions for the second test, the same 3 questions will be chosen as for the first?

Final Answer:

p =  0.0877 %

Step-by-step explanation:

$$\begin{gathered} C_3(20)=\left(\genfrac{}{}{0ex}{}{20}{3}\right)=\frac{20!}{3!(20-3)!}=\frac{20\cdot 19\cdot 18}{3\cdot 2\cdot 1}=1140 \\ n=\left(\genfrac{}{}{0ex}{}{20}{3}\right)=1140 \\ {n}_2=1 \\ p=100\cdot \frac{n_2}{n}=100\cdot \frac{1}{1140}=\frac{100\cdot 1}{1140}=\frac{100}{1140}=0.0877\% \end{gathered}$$

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