Probability 80858

During the exam, the student takes 3 questions out of 30. He is ready for 20 of them. Find the probability that he draws at most 2 that he knows.

Correct answer:

p =  0.7037

Step-by-step explanation:

$$\begin{gathered} r=\frac{20}{30}=\frac{2}{3}\doteq 0.6667 \\ {p}_0=\left(\genfrac{}{}{0ex}{}{3}{0}\right)\cdot r^0\cdot (1-r{)}^{3-0}=(\genfrac{}{}{0ex}{}{3}{0})\cdot 0.6667^0\cdot (1-0.6667{)}^{3-0}=1\cdot 0.6667^0\cdot 0.3333^3=\frac{1}{27}\doteq 0.037 \\ {p}_1=\left(\genfrac{}{}{0ex}{}{3}{1}\right)\cdot r^1\cdot (1-r{)}^{3-1}=(\genfrac{}{}{0ex}{}{3}{1})\cdot 0.6667^1\cdot (1-0.6667{)}^{3-1}=3\cdot 0.6667^1\cdot 0.3333^2=\frac{2}{9}\doteq 0.2222 \\ {p}_2=\left(\genfrac{}{}{0ex}{}{3}{2}\right)\cdot r^2\cdot (1-r{)}^{3-2}=(\genfrac{}{}{0ex}{}{3}{2})\cdot 0.6667^2\cdot (1-0.6667{)}^{3-2}=3\cdot 0.6667^2\cdot 0.3333^1=\frac{4}{9}\doteq 0.4444 \\ p=p_0+p_1+p_2=0.037+0.2222+0.4444=0.7037 \end{gathered}$$

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